电池温度场特性估计

Thermal runaway is a growing concern in the field of Lithium ion batteries. To address this, temperature measurement is the most direct method. However, placing temperature sensors on each cell of a battery pack may be impractical. An alternative is to estimate temperature of a cell by using Electrochemical Impedance Spectroscopy (EIS). Literature has shown that the phase of the impedance of the cell can be correlated to its internal temperature, but a simple procedure to identify the frequency at which the phase should be calculated has not been reported. In this work, a methodology is developed to identify the frequency at which the phase of the impedance of the cell should be calculated by using the Distribution of Relaxation Times (DRT) technique. The methodology has also been validated on cells of different form factors (cylindrical and pouch) and also for cells under load.

This study focuses on the internal temperature field of lithium-ion batteries, aiming to address the temperature variation issues arising from complex operating conditions in new energy batteries. To cope with unpredictable temperature fluctuations and long delay times, we propose an enhanced Convolutional Bidirectional Long Short-Term Memory Neural Network (CNN-Bi-LSTM-AM) model for temperature field prediction. The model integrates CNN for spatial feature extraction, Bi-LSTM for capturing temporal characteristics, and an attention mechanism to enhance the identification of key time-series features. By simulating temperature variations through a lumped model and thermal runaway model, we generate temperature field data, which are then utilized by the deep learning model to effectively capture the complex nonlinear relationships between temperature, voltage, state of charge (SOC), insulation resistance, current, and the internal temperature field. Performance evaluation using accuracy metrics and validation under various environmental conditions demonstrates that the model improves prediction accuracy by 1.2–2.3% compared to traditional methods (e.g., ARIMA, LSTM) with only a slight increase in testing time. Comprehensive evaluations, including ablation studies, thermal runaway tests, and computational efficiency analysis, further validate the robustness and applicability of the model. Furthermore, this study contributes to the optimization of battery life and safety by enhancing the prediction accuracy of the internal temperature field, thereby reducing resource waste caused by battery performance degradation. The findings provide an innovative approach to advancing new energy battery technology, promoting its development toward greater safety, stability, and environmental sustainability, which aligns with global sustainable development goals.

We propose a method that relates to a real-time monitoring method for internal temperature of a battery pack based on compression sensing and deep learning theory, belonging to the technical field of battery pack thermal management. According to the experimental temperature of all positions when charging, discharging and under different load conditions for the same type of battery pack, we apply the neural network algorithm in deep learning to train the simulated temperature field model which is suitable for the specific kind of battery packs. Then we call the model by software to predict the temperature of all the positions in the battery packs, thereby completing global real-time monitoring of the internal temperature of the battery packs. In this paper, we use “DNN”, “LSTM”, and machine learning algorithms to achieve the compressive sensing of the battery packs. The results show that the "LSTM" algorithm requires 32-channel detection, with its average absolute error between the predicted result and the actual detection result is $0.21^{\circ}C$ and the maximum error is $1^{\circ} C$. The “DNN” algorithm only needs 8 channels for detection and the average absolute error between the prediction result and the actual detection result is $0.25^{\circ} C$. This algorithm has an excellent application prospect in the field of battery pack thermal management and real-time condition detection of power batteries packs.

With the increasing size of lithium-ion batteries (LIBs), more temperature sensing points can be deployed to capture a comprehensive thermal profile, enabling more accurate monitoring of battery states. However, traditional internal short circuit (ISC) recognition methods often exhibit limited sensitivity to early-stage micro short circuits, delayed response, and vulnerability to external thermal disturbances, leading to false alarms or missed detections. To address these issues, this study proposes an early ISC identification method that integrates a thermal resistance network model with a cosine similarity-based diversity analysis, and the model-predicted temperature field is used as a reference baseline. Then, a dissimilarity index based on cosine similarity is introduced to dynamically monitor local deviations in the measured temperature matrix, thereby enabling early identification of micro short circuits. Meanwhile, by analyzing the evolution trend of discrepancies between the measured and predicted temperature fields, the method can effectively identify internal fault symptoms even under weak external thermal disturbances. Furthermore, by simulating the initial thermal behavior of an ISC through local heating experiments using electric heating wire, the results show that the proposed method achieves higher accuracy, robustness, and response speed than conventional temperature difference or gradient-based approaches, particularly for micro short circuits. This method not only improves the sensitivity and reliability of micro short circuit recognition but also provides a promising solution for digital thermal safety monitoring of large-sized LIBs.

Lithium-ion (Li-ion) batteries dominate the EVs field due to unique features like high power and energy density, excellent storage capabilities and memory-free recharge characteristics. Despite that, assorted phenomena affect the reliability of battery packs at high temperatures, causing efficiency loss, danger of explosions and rapid degradation. Consequently, it is necessary to understand the thermal behaviour of Li-ion batteries under specific discharge and charge conditions for operating in critical hot spots, dissipating the generated heat and decreasing the average temperature and internal temperature spans. This paper contributes to developing a thermal model for Li-ion batteries subjected to any discharge and charge current profile, estimating the generated heat, the dissipated heat in natural convection, the average temperature and the maximum internal temperature span. These results have been obtained by coupling the widely known Equivalent Circuit Model (ECM) with the Bernardi et al. equation, which permits estimating the heat generated by any battery cell, knowing the voltage drops caused by ohmic and polarisation losses. The results were validated through two tests conducted on a 1500 mAh LTO cell, whose ECM was obtained through an experimental characterisation by following the HPPC procedures. As a result, the model reached percentage errors below ± 7%. This approach defines a necessary initial step to characterise the maximum average temperature reachable by the Li-ion cell, verifying if this value overcomes the acceptable working limit.

Storage batteries with elevated energy density, superior safety and economic costs continues to escalate. Batteries can pose safety hazards due to internal short circuits, open circuits and other malfunctions during usage, hence real-time surveillance and error diagnosis of the battery’s operational state is imperative. In this paper, a three-dimensional model of electrochemical-magnetic field-thermal coupling is formulated with lithium-ion pouch cells as the research focus, and the spatial distribution pattern of the physical field such as magnetic field and temperature when the battery is operational is acquired. Furthermore, this manuscript also investigates the diagnostic methodology for defective batteries with internal short circuits and fissures, that is, the operational state of the battery is evaluated and diagnosed by the distribution of the magnetic field surrounding the battery. To substantiate the method’s practical viability, the present study extends its examination to the 18650-battery pack. We obtained the magnetic field images of the normal operation of the battery pack and the failure state of some batteries and analyzed the relationship between the magnetic field distribution characteristics and the performance of the battery pack, providing a new method for the health monitoring and fault diagnosis of the battery pack. This non-contact method incurs no damage to the battery, concurrently exhibiting elevated sensitivity and extremely rapid response time. Meanwhile, it provides an effective means for non-destructive research on the batteries and can be applied to areas such as battery safety screening and non-destructive testing. This research not only helps to facilitate our understanding of the battery’s operating mechanism, but also provides robust support for safe operation and optimal battery design.

Lithium-ion batteries are widely used in new energy vehicles, especially electric vehicles. Temperature estimation is very important for battery life and safety. However, current temperature measurement methods cannot accurately measure the battery internal temperature. In this paper, a new method for battery temperature estimation based on an improved magnetic nanoparticle thermometer (MNPT) is proposed. The influence of dc magnetic field on temperature accuracy of a MNPT is firstly studied, the optimal dc magnetic field is found out under limitation of maximum temperature sensitivity and minimum temperature error, a new model of an improved MNPT is also established based on the ratio of first and second harmonics, and then the Lithium-ion battery temperature is estimated by use of the improved MNPT, the simulation and experiment results show that the improved MNPT can accurately estimate the battery internal temperature, which provides a new method for monitoring battery temperature of a new energy vehicle.

Accurate modelling of electric vehicle battery systems is essential for optimising performance, improving efficiency, and extending battery life as electric vehicles become increasingly popular as environmentally friendly transportation options. This study explores the complex field of mathematical modelling as it pertains to electric vehicle batteries. The goal is to offer a thorough summary of the different methods, obstacles, and future possibilities in this important field. The paper thoroughly analyses past developments and current battery models, explaining the transition from traditional methods to modern physics-based models. Exploring the core electrochemical mechanisms that impact battery performance, emphasising important factors like internal resistance, state of charge, and temperature effects. Examining various modelling techniques, this analysis discusses the advantages and disadvantages of each approach. The methods discussed encompass physics-based, empirical, and hybrid models. Investigating the complex interplay between electrochemistry, thermal effects, and external factors that impact battery performance is the focus of this study. The study also explores the relationship between these models and the dynamic characteristics seen in electric vehicle batteries. This study contributes to our comprehension of the mathematical modelling of batteries in electric vehicles.

Internal temperature monitoring of battery cells can be very useful, as the core temperature can deviate significantly from that of the housing, especially in case of cells with a thick electrode stack. Conventional resistance temperature detectors can accurately measure temperature, but are limited to the outer surface of the cell due to induction effects. They are therefore not suitable for internal in situ measurements. Fiber Bragg grating (FBG) sensors are unaffected by the electric field as they operate by reflecting light. However, a specific difficulty is the distinction of temperature vs. strain effects as the grating is sensitive to both. In this work a calibration routine to separate the influences of temperature and strain in a lithium-ion battery cell is presented and examined for two multi-layer stack pouch cells (10 and 20 Ah). The obtained in situ temperature data reveal a difference of up to 2°C between center and cell housing at elevated discharge rate (4C) and a delay in detection of temperature peaks by the external sensor by 12 s. Strain data correlate with numbers of electrode layers in the stack and yield a stress of up to 27.3 MPa in the center of the 20 Ah cell.

The performance of lithium-ion batteries is greatly influenced by various factors within their operating environment, which can significantly impact their overall efficiency and effectiveness. In this paper, a multi-physics field electrochemical thermal model is established to measure the physical parameters of a battery module during the charge/discharge process. The effects of working temperature, current rate, and convective heat transfer coefficient are investigated by establishing an electrochemical and thermal model. The results are obtained by conducting numerous parameterized scans to analyze the system’s state across various operating conditions, enabling the determination of its temperature and the selection of appropriate cooling measures accordingly. Based on the internal and external conditions of battery operation, parameter selection corresponding to the operating range is divided into several stages, with thermal management strategies provided for each stage. The existing framework facilitates the design of battery packs equipped with efficient thermal management strategies, thereby enhancing the battery systems’ reliability and performance. Furthermore, it aids in establishing optimal operational and safety boundaries for batteries.

Liquid metal battery (LMB) is considered a promising grid-level energy storage technology due to its low cost, long lifespan, and feasible amplification. As an all-liquid battery, the mechanisms and effects of its internal flow still need to be further studied. In this work, we establish two-dimensional (2D) axisymmetric models coupling both the thermal field and electromagnetic field based on Li|LiCl-KCl|Bi system. The fluid motions inside the batteries driven by temperature field, electromagnetic field, and coupled field are analyzed contrastively, revealing the dominant role of thermal convection. Moreover, the effects of the flow driven by different physical fields on the electrochemical reaction process are investigated. Those results are of great significance for further understanding the electrochemical process of LMB and other battery systems and optimizing the battery performance.

Aiming at the problems of large internal heat generation and uneven heat dissipation of cylindrical power battery module of electric vehicle, a new divergent heat dissipation model of cylindrical battery is proposed. A certain type of 18650 batteries is taken as an example to simulate and analyze its temperature field. The results show that the temperature distribution law of batteries located on the same concentric circle is almost the same. For the single cell, the overall temperature distribution shows the following law: the temperature gradually decreases from inside to outside of the battery. The temperature gradually decreases from top to bottom of the battery . The temperature near the center of the flow field is low. The temperature away from the center of the flow field is high. The change rate of the maximum temperature and the maximum temperature difference of the battery pack gradually decreases with the increase of mass flow rate. The change rate of the maximum temperature and the maximum temperature difference of the battery pack gradually decreases with the increase of the center distance. And the lowest is -1.59% and -14.95%. It provides a reference for the future research on heat dissipation of cylindrical battery

Abstract Impedance-based temperature detection (ITD) is a promising approach for rapid estimation of internal cell temperature based on the correlation between temperature and electrochemical impedance. Previously, ITD was used as part of an Extended Kalman Filter (EKF) state-estimator in conjunction with a thermal model to enable estimation of the 1-D temperature distribution of a cylindrical lithium-ion battery. Here, we extend this method to enable estimation of the 2-D temperature field of a battery with temperature gradients in both the radial and axial directions. An EKF using a parameterised 2-D spectral-Galerkin model with ITD measurement input (the imaginary part of the impedance at 215 Hz) is shown to accurately predict the core temperature and multiple surface temperatures of a 32,113 LiFePO4 cell, using current excitation profiles based on an Artemis HEV drive cycle. The method is validated experimentally on a cell fitted with a heat sink and asymmetrically cooled via forced air convection. A novel approach to impedance-temperature calibration is also presented, which uses data from a single drive cycle, rather than measurements at multiple uniform cell temperatures as in previous studies. This greatly reduces the time required for calibration, since it overcomes the need for repeated cell thermal equalization.

Nonuniform thermal behavior in lithium-ion battery packs can accelerate aging, leading to inconsistent cell performance. If not adequately monitored and managed, this heating can give rise to unwanted side reactions, fires, and explosions, underscoring the criticality of temperature field reconstruction. In recent years, data-driven methods have gained popularity for addressing the temperature field reconstruction problem. However, many existing data-driven approaches require retraining when system parameters change, such as the initial temperature distribution or working conditions. This article presents a deep transfer operator learning method named physics-informed adversarial networks. The model architecture incorporates transformer blocks to capture comprehensive time and space features. Additionally, to enhance interpretability and generalization, the model introduces two effective mechanisms: 1) the integration of thermal partial differential equations to ensure compliance with physical laws; and 2) the application of domain adversarial mechanism in transfer learning to extract domain-invariant feature representations. These mechanisms enable the model to effectively reconstruct the temperature field, even in unencountered scenarios during training. The proposed method is validated under real-world energy storage working conditions, demonstrating superior performance compared to state-of-the-art deep learning methods. Notably, the approach exhibits excellent performance even when confronted with the limited availability of training data.

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Lithium-ion batteries pose a risk of thermal runaway (TR) during operation. Monitoring the temperature distribution within the battery is crucial for ensuring thermal safety and preventing such runaway events. However, constructing the temperature field typically requires a large amount of sensor data and is challenging to perform in real time. To address this issue, this article proposes a novel method for reconstructing the temperature field of lithium-ion batteries during TR using a sparse random-sensor mask autoencoder (SRS-MAE). This approach enables real-time reconstruction of the battery’s complete pixel-level temperature field using minimal sensor data. Additionally, this article explores the impact of sensor location and quantity on the model’s reconstruction accuracy, providing a theoretical basis for optimizing the position of temperature sensors in actual battery management systems. This article employs an experimental-simulated thermal image dataset to validate the method’s superiority and reliability. The results demonstrate that the SRS-MAE can accurately predict the battery’s TR temperature field, requiring data from as few as two sensors to reconstruct the complete pixel-level temperature field of the battery. Given the critical need for efficient and accurate temperature monitoring in battery systems, the SRS-MAE method offers a vital solution for battery temperature field reconstruction and advancing the capabilities of battery management systems.

As lithium-ion batteries are widely used in different fields, the thermal effect is of serious concern. How to achieve accurate temperature estimation in real time is the main challenge of current research. To address this problem, we propose a real-time distributed moving horizon estimation (RT-DMHE) based on partial differential equations describing thermal dynamics of a lithium-ion battery pack. It decomposes the real-time centralized moving horizon estimation (RT-CMHE) into multiple local estimators that run in parallel with information exchange from adjacent subsystems. Simulation validation shows that the root mean square error of temperature estimates from the proposed RT-DMHE is smaller than that of an existing distributed Kalman filter in literature. Moreover, compared to the RT-CMHE, the proposed RT-DMHE achieves comparable estimation accuracy while vastly reducing the average computation time per sample.

Despite the ever-increasing use across different sectors, the lithium-ion batteries (LiBs) have continually seen serious concerns over their thermal vulnerability. The LiB operation involves heat generation and buildup effect, which manifests itself strongly, in the form of highly uneven thermal distribution, for a LiB pack consisting of multiple cells. If not well monitored and managed, the heating may accelerate aging and cause unwanted side reactions. In extreme cases, it will even cause fires and explosions. Toward addressing this threat, this brief, for the first time, seeks to reconstruct the 3-D temperature field of a LiB pack in real time. The major challenge lies in how to acquire a high-fidelity reconstruction with constrained computation time. In this brief, a 3-D thermal model is established first for a LiB pack configured in series, which captures the spatial thermal behavior with a combination of high integrity and low complexity. Given the model, the standard Kalman filter is then distributed to attain temperature field estimation with substantially reduced computational complexity. The arithmetic operation analysis and the numerical simulation illustrate that the proposed distributed estimation achieves a comparable accuracy as the centralized approach but with much less computation.

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Real‐time and accurate temperature monitoring has been widely recognized in both academia and industry to ensure battery operation safety. Traditional techniques are generally limited to incomplete information caused by discrete sampling points. Hence, the spiral‐serpentine distributed optical fiber sensor (DOFS) layout is presented to realize in‐situ full‐range temperature measurement. Unlike conventional contact‐based sensors, DOFS offers high spatial resolution with 1.28 mm for comprehensive‐accurate monitoring. The proposed deployment enables mapping across the entire surface, rather than being restricted to certain points or localized regions. Meanwhile, the locally adaptive radial basis function interpolation algorithm is developed to reconstruct temperature filed, which aims to ensure the global smoothness and local variability. Uncertainty quantification is incorporated to enhance the results reliability. Experimental studies are conducted on large‐format pouch LIBs used in BYD electric vehicles under various currents. The results demonstrate that it can accurately and in real‐time capture temperature variations. The developed reconstruction method precisely acquires the full‐field temperature distribution with a max standard deviation below 0.3 ℃. Detailed comparison with other six measurement‐reconstruction methods such as thermocouple (TC), infrared thermography (IT), Fiber Bragg Grating (FBG) and different‐shaped DOFS further highlights the superiority. This work offers significantly valuable insights for optimizing battery thermal management systems.

The lithium-ion battery (LIB) is a complex multiphysics system, wherein real-time monitoring of its internal thermal behavior remains a fundamental challenge. Traditional thermal modeling approaches, especially those employing high-resolution simulations, have been widely adopted to capture detailed spatial temperature distributions. However, the substantial computational burden associated with such methods hinders their applicability for real-time thermal field reconstruction. In this study, we propose a generative thermal reconstruction (GenTR) framework that synergistically integrates artificial intelligence (AI) with physics-based modeling to address this limitation. GenTR enables the real-time generation of dynamic, high-resolution thermal field distributions ( $128\times 128$ pixels) directly from coarse-resolution physics-informed inputs ( $8\times 8$ nodes). For the first time, the proposed GenTR framework enhances conventional generative AI (GAI) approaches by integrating rigorous physics-based guidance, thereby enabling real-time reconstruction and visualization of internal temperature fields with only 150 iteration steps. The method supports high-resolution, image-based thermal field generation while preserving physical consistency. The effectiveness of GenTR is experimentally validated on practical battery cells under both static and dynamic operating conditions. Across all test scenarios, the mean absolute percentage errors remain below 1%, demonstrating its accuracy and reliability. Comparative analyses further reveal that GenTR not only resolves the convergence limitations inherent in conventional numerical models but also significantly enhances the fidelity and robustness of GAI-based thermal estimation approaches.

High-capacity and large-sized batteries are widely employed in electric vehicles and energy storage systems. The surface temperature field of these batteries is usually maldistributed and unmeasurable in practice, which brings great challenges to temperature safety monitoring. Thus, this article rebuilds the lumped thermal model and proposes a Kalman filter (KF)-multilayer perception (MLP) joint estimation algorithm to reconstruct the 2-D ST field of lithium-ion batteries (LIBs). First, an improved lumped thermal model is devised to accurately obtain multipoint temperatures with only one sensor. Then, a KF-MLP neural network is proposed to diminish the utilization of computational resources and enhance the model generalization capability. Finally, a 2-D temperature acquisition method is designed to obtain reliable experiential data. Experiments are designed to demonstrate the effectiveness of the proposed lumped thermal model-based KF-MLP estimation algorithm. Under 5 <inline-formula><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula>C discharge conditions for square LIBs, the maximum average error between estimated and actual temperatures on the battery surface is 0.0761 <inline-formula><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula>C.

Large prismatic cells are increasingly being used as the primary power source in transportation applications. Effective online thermal management of these cells is crucial for ensuring safety and maximizing performance. However, significant discrepancies between surface and internal temperatures make it difficult to detect internal thermal anomalies promptly, which hinders effective thermal management and increases the risk of irreversible thermal hazards. This paper introduces an innovative technology for thermal management in prismatic Li‐ion batteries. By exploiting the temperature sensitivity of ultrasound velocity and applying tomographic reconstruction based on surrounding measurements, the technology enables detailed cross‐sectional thermal imaging. This allows for non‐destructive, real‐time visualization of internal temperatures. Furthermore, with its compact design and cost‐effectiveness, this technology is suitable for in‐situ deployment, offering a precise feedback mechanism for online thermal management. Demonstrations conducted during continuous discharging scenarios have shown that the system can identify high‐temperature regions near the tabs that remain undetected by surface thermocouples. This advancement has the potential to significantly reduce the risk of fires or explosions while enhancing battery performance in electric vehicles and other applications involving battery cells.

Current battery management system (BMS) often takes the battery pack surface temperature as the judgment basis for algorithm design, and cannot sense the temperature change inside the lithium battery pack (LBP), resulting in the inability to predict thermal faults in a timely manner and prevent thermal runaway. To solve this issue, this article proposes a novel method for estimating the internal temperature distribution of LBP under air-cooling conditions. First, the thermal resistance heat transfer models for the internal and boundary batteries of LBP were developed by using the thermal equilibrium theory. This modeling process comprehensively considers the complex heat transfer and dissipation characteristics of individual batteries in the battery pack, which can improve the interpretability of the modeling process. Next, a state-space model for estimating the temperature distribution of LBP was constructed by combining the heat transfer models of internal and boundary batteries. Finally, a novel dual time scale multi-innovation extended Kalman filter (EKF) observer was proposed for collaborative estimation of the battery pack temperature and convection coefficient, which can provide disturbance compensation for state estimation. Experiments and verification indicate that the proposed method is effective and has better estimation ability compared with the other method under different cycles, and the estimation error is less than 2°C.

In recent years, lithium-ion batteries (LIBs) have been massively developed in many applications as they provide high energy and power densities, high efficiency and long lifespan compared to other battery technologies. Despite remarkable improvements, Li-ion batteries still face thermal issues, which cause performance drop, limited calendar life, safety concerns and temperature-caused degradation. Therefore, proper thermal management for a LIB is necessary to control its temperature and to extend its lifetime. Internal temperature measurement remains very challenging for LIB. So, electrothermal LIB models, developed to forecast both electrical performances and temperature distributions, seems to be a powerful and complementary tool to experiments, in particular to obtain battery temperatures in use. Most of models, assume simplified approach considering that heat sources are either located in the center of the cell or uniformly distributed in the volume of the cell and so do not consider the real internal geometry of the cells. In this work, a 3D electrothermal model of a large commercial prismatic NMC-type lithium-ion cell (25 Ah) is developed based on the internal geometry reconstructed from tomography. The electrothermal model, developed with the COMSOL Multiphysics® software with the real internal geometry as well as the anisotropy of the thermal properties, accounts for irreversible and reversible heat sources. The entropy variation profiles were estimated by Entroview™ using their patented method. The validation of the model is performed thank to temperature measurement during charge and discharge at several currents in a climatic chamber at 25°C. Simulation results highlight exothermal and endothermal behaviors related to the entropy change along with the charge and discharge stages. Moreover, the internal temperature distribution is thoroughly impacted by the internal geometry of the cell and the anisotropy of the thermal properties. Finally, the 3D electrothermal model is extended to a module of 12 cells in series (12S) to evaluate the heterogeneities of internal temperatures considering the real geometry of each cell. Once validated, simulation (as shown of figure 1) underline the heterogeneous temperature distribution at the module scale and the importance of having an efficient battery thermal management system to limit an excessive increase of the temperatures which can cause performance drops until irreversible degradations. Figure 1

The large-scale deployment of lithium-ion batteries necessitates careful thermal management to ensure safety, performance, and longevity. Internal thermal gradients can pose safety risks and accelerate battery degradation, making internal temperature monitoring both critical and challenging. This paper presents a physics-informed neural network approach that enables accurate, real-time, and high-resolution estimation of the internal temperature distribution within LIBs by integrating sparse sensor measurements with governing physical laws. The proposed framework leverages the complementary strengths of data-driven learning and physics-based modeling, allowing a lightweight neural network to match or even surpass the performance of the full-order model in internal temperature estimation. Furthermore, the proposed method demonstrates robustness to imperfect physics-based prior knowledge, offering a practical and scalable solution for advanced battery thermal monitoring.

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Charge time has become one of the primary issues restricting the development of electric vehicles. To counter this problem, an adapted thermal management system needs to be designed in order to reduce the internal thermal gradient, by predicting the surface and internal temperature responses of the battery. In this work, a pseudo 3D model is developed to simulate battery cell performance and its internal states under various operational scenarios such as temperature and convection conditions as well as the applied current during charge and discharge. An original mesh of the JR is proposed where heat exchanges in the three directions (radial, orthoradial and axial) are considered. The model represents one of the solutions that enable increasing the lifespan of batteries while decreasing charging time. It offers the opportunity to optimize operating parameters to extend battery life. In this paper, attention was paid not only to the core and non-core components, but also to the experiments required to parametrize the thermal and electrochemical models (heat generation). Unlike existing approaches documented in the literature, the model developed in this work achieves an impressive balance between computational efficiency and result accuracy, making it a groundbreaking contribution in the field of electric vehicle technology.

In the domain of Battery Management System (BMS) research, the precise acquisition and estimation of internal temperature distribution within lithium-ion cells is a significant challenge. The commercial viability precludes the use of internal temperature sensors, and existing methodologies for online estimation of internal temperatures under various electrical loads are constrained by computational limitations and model accuracy. This study presents a layered electro-thermal equivalent circuit model (LETECM), developed by integrating a layered second-order fractional equivalent circuit model with a layered thermal equivalent circuit model. A lithium-ion battery divided into three layers was employed to illustrate the development of this LETECM. The model’s precision was validated against a 3D Newman Finite Element Model (3DNFEM), constructed using actual battery parameters. Given that the thermal gradient inside the battery is usually more pronounced under high load conditions, a 10C direct current discharge for 60 s followed by a rest period of 240 s was adopted as the test condition in the simulation. The results indicate that at the end of the DC discharge, the temperature difference between the inner layer and the surface of the battery was the largest and the maximum temperature difference predicted by the LETECM was 3.58 °C, while the 3DNFEM exhibited a temperature difference of 3.74 °C. The trends in each layer temperature and battery surface temperature obtained by the two models are highly consistent. The proposed model offers computational efficiency and maintains notable accuracy, suggesting its potential integration into BMS for real-time online applications. This advancement could provide critical internal temperature data for refining battery charging and discharging performance assessments and lifespan predictions, thereby optimizing battery management strategies.

Lithium-ion batteries (LIBs) are central to modern energy storage systems, yet accurate monitoring of their internal thermal behavior remains a challenge. This study proposes an advanced method for measuring and predicting core temperature variations in 18650 LIB cells, addressing the limitations of conventional surface-based temperature measurements and thermal imaging techniques. An innovative hermetically sealed measurement fixture was developed to enable direct, localized, and stable internal heat distribution monitoring under vacuum conditions, mitigating electrolyte evaporation and oxidation risks. A refined lumped thermal-electrical model incorporating both radial and axial heat conduction paths was proposed and validated through empirical experiments. The proposed measurement method was conducted to evaluate the feasibility of the method, and the proposed lumped model was also experimentally validated using the IMREN 18650-3500-30A battery (with a nominal capacity of 3500 mAh and a maximum continuous discharge rate of 10 A). The results demonstrated a maximum accuracy improvement of up to 8.23% during the transient period. The proposed approach offers valuable insights for enhancing battery thermal management strategies, improving thermal simulation accuracy, and informing safer, more efficient battery designs.

Lithium-ion batteries are the crucial energy source for electric vehicles. However, they experience capacity degeneration when used in low-temperature environments. It is necessary to preheat them before using. In this paper, a core temperature-aware optimal preheating strategy, featuring a multi-stage constant-current discharge heating method, is proposed to heat lithium-ion batteries in low-temperature environments. Firstly, this paper builds an internal battery temperature distribution model based on Fourier’s law of heat conduction. Secondly, the temperature distribution model is coupled within the battery model to display the comprehensive performance of the battery. Thirdly, decreasing heating time and reducing capacity loss jointly formulate a multi-objective optimization problem solved by dynamic programming(DP) algorithm. Judging by simulation results, heating time is downsized and the capacity loss is reduced at the same time, proving the progressiveness of the proposed strategy.

Nonuniform temperatures in lithium-ion battery modules, caused by manufacturing inconsistencies, vibrations, and unequal line resistances, lead to uneven current distribution and accelerated degradation of the battery. Existing thermal management methods face challenges in achieving real-time cell-level balancing due to limited intercell modeling, high computational cost, and lack of closed-loop control. This article proposes a model predictive temperature balancing control (MPTBC) strategy based on a scalable 2-D thermal network model (TNM) that captures intercell thermal coupling and enables real-time prediction with reduced computational cost. A physics-informed neural network (PINN) models the nonlinear internal resistance, with Bayesian optimization (BO) used to efficiently identify optimal parameters. The MPTBC is implemented on a four-module, high-power-density, single-input multioutput (SIMO) switched-capacitor (SC) converter. Experiments validate the TNM accuracy and demonstrate that MPTBC effectively minimizes cell-to-cell temperature differences.

A coupled electrochemical-thermal model based on the pseudo-two-dimensional (P2D) structure of lithium-ion batteries was established using Multiphysics to simulate and analyze the spatial and temporal distribution of temperature during battery operation. Based on the simulation results, critical locations that comprehensively represent the thermal characteristics of the battery were selected for temperature monitoring. Accordingly, a temperature sensing system based on fiber Bragg grating (FBG) was designed and implemented. FBG sensors were embedded at the anode, cathode, and the central symmetry axis of pouch-type lithium-ion batteries to collect and analyze internal temperature data. Temperature monitoring was carried out under various current conditions for batteries equipped with embedded FBG sensors. Experimental results revealed a characteristic double-peak fluctuation in internal temperature during a full charge-discharge cycle—rising, then falling, and again rising before finally decreasing, reaching its maximum at the cycle’s end. Long-term operational tests demonstrated that the FBG sensors, while ensuring normal charge and discharge cycles, reliably provided real-time, high-precision measurements of internal temperatures. These findings are consistent with results obtained from simulation analysis. The proposed methodology offers robust technical support for the optimization and advancement of lithium-ion batteries, significantly enhancing research and maintenance efficiency.

Lithium ion batteries are widely used in energy storage systems because of their fast response, high energy density and other characteristics. However, during the charging and discharging process of lithium battery, the internal chemical reaction rate is accelerated, and more heat is generated, resulting in the rapid rise of battery temperature, which affects the safety of the battery. In order to effectively solve the overheating problem of lithium-ion battery in the process of charging and discharging, and ensure the safety and performance stability of the battery, the lumped parameter thermal model of 280 Ah lithium iron phosphate battery was established, and the temperature distribution and its change law in the battery were analyzed. The adaptive weighted particle swarm optimization (AWPSO) algorithm was used to identify the parameters of the thermal model to improve the accuracy of the model. The battery thermal model was built in Matlab/Simulink, and the temperature error was 0.6 °C through the comparison of simulation experiments, which provided theoretical basis and technical support for the battery thermal management system.

Large-format prismatic lithium iron phosphate (LFP) batteries hold significant potential in energy storage systems. However, heat accumulates near the tabs when the LFP battery cell is operating, resulting in non-uniform temperature distribution within the cell. Optimizing the tab configuration is crucial for ensuring battery lifespan and preventing thermal runaway. Due to the complexity of the internal structure, existing research mainly focuses on the tab design of pouch cells, with limited studies on prismatic cells. In this work, a 3D electrochemical-3D thermal coupled model for 280 Ah prismatic LFP battery cell was developed and validated with experimental data. The effects of tab width and thicknesses on the thermal performance of the battery were investigated, and the optimal tab dimensions were determined. The results indicate that increasing the tab width from 3 cm to 7 cm significantly reduces the maximum temperature (Tmax) and temperature difference (ΔTmax) by 39.32% and 81.18%, respectively, with diminishing benefits at wider levels. Additionally, the regions of high current density are primarily concentrated near the positive tab. The augment of the tab thickness significantly enhances current uniformity and reduces Joule heating near the tabs, resulting in lower Tmax and ΔTmax. However, the improvements diminish as thickness continues to increase. Furthermore, the optimized configuration, featuring a 7 cm tab width and tab thicknesses of 12 μm for negative and 16 μm for positive, achieved substantial reductions in Tmax and average temperature, along with a ΔTmax of 4.1°C, effectively enhancing cell temperature uniformity compared to the original design. The proposed model and findings are expected to provide guidance for the design and optimization of large-format LFP batteries.

Accurate modeling and estimation of the internal temperature distribution is of great significance to the thermal management of lithium-ion batteries (LIBs). Existing control-oriented models generally assume a uniform temperature distribution along the axial direction of LIB. The ignorance of thermal inhomogeneity, however, challenges the refined thermal monitoring of LIB. To remedy this deficiency, this article proposes for the first time a novel distributed thermal model for LIB, by hybridizing the thermal transfer law and the artificial intelligence approach. Relying on the spatial temperatures of LIB obtained by a distributed sensing technique, a lumped-parameter thermal network model is developed to capture the general thermal behavior of LIB. In a cascaded manner, the long short-term memory (LSTM) neural network is proposed to compensate for the thermal inhomogeneities that cannot be explained. The proposed cascaded distributed thermal (CDT) model further proves to be compatible with commonly used observers for online internal temperature distribution estimation. Experimental results suggest that the proposed distributed model and the associated estimation framework can give space-resolved inner temperature estimation with remarkably improved accuracy compared with the existing methods.

No abstract available

The increasing events of fire and catastrophic failure of lithium-ion batteries (LIBs) due to inaccurate thermal information or improper thermal management based on surface temperature data only, once again indicates the necessity of accurate core temperature information. In view of this, a rapid, more convenient but accurate thermal modeling technique for LIB is introduced in this paper using SIMBA. SIMBA is a powerful new generation power electronics simulation software powered by Python. A second-order electro-thermal model-based core temperature estimation scheme is developed in SIMBA. A wide range of battery test data is used for experimental validation of the model. Further, four standard drive cycle profiles are used to assess the impact of discharge current on the core temperature of LIB. The electro-thermal model allows estimating the core temperature from external measurements including voltage, current, and surface temperature without installing a physical core temperature sensor which is practically challenging. The proposed modeling technique is extremely convenient and the model is computationally efficient and simple enough to be implemented in practical purpose lithium-ion battery management systems.

Lithium-ion batteries and their control technologies are the key points to electrification and intelligence of transportation. Dynamic thermal management is one of the key technologies for intelligent battery management systems. Real-time monitoring of information about the temperature characteristics inside the battery is important for effective and safe thermal management. This article fist constructs a distributed control-oriented electro-thermal coupling model that contains multidimensional internal information about the cell. Based on the proposed model, improved parameter identification methods are used to construct offline database of model parameters. The electrical and thermal parameters are identified by applying recursive least squares with variable forgetting factor and particle swarm optimization separately. Finally, a state of charge (SoC)-modified core temperature estimation method is proposed, which adopts discrete-time nonlinear observer to modify SoC and adaptive Kalman filter to estimate core temperature. The method takes into account the sensitivity of the output results to nonlinear, time-varying battery systems. The results show that the root-mean-square error (RMSE) of SoC estimation is 1.75% and the mean absolute error (MAE) is 0.65% for the proposed temperature method under wide temperature points (−5 °C, 25 °C, and 45 °C). The proposed core temperature estimation method possesses better robustness and universality, with RMSE of 0.61 °C and MAE of 0.56 °C. Compared with the open-loop prediction method, the accuracy is improved about 0.5 °C under extreme loadfiles with uncertainty.

Lithium-ion batteries (LIBs) are a widely used energy storage technology owing to their excellent energy density, minimal self-discharge property, and high cycle life. Despite these promising features, their performance is affected by both low and high temperatures. When the internal temperature exceeds a certain threshold, the battery may experience thermal runaway, leading to fire and explosion. Moreover, this process is accelerated at high charge/discharge currents. Therefore, in high current applications, accurate monitoring of the internal temperature of the battery becomes critically important to ensure the safety. Hence, an improved coupled electrothermal model (ICETM) has been proposed by combining a novel three-state thermal model with an existing electrical equivalent circuit model through temperature dependent electrical parameters and heat generation. The primary aim is to improve the accuracy of internal temperature estimation of the battery at high currents while accounting for time efficiency in thermal model parameterization. The ICETM is parameterized through experimental and simulation studies using a LiFePO4/graphite battery. The effectiveness of the proposed model and parameterization method is validated experimentally using two case studies. The results show 14% improvement in accuracy and 140–160 hours time reduction over its existing counterparts in estimating core temperature and model parameterization, respectively.

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Accurate and efficient estimation of the battery core temperature is essential for the reliable and safe battery system. However, restricted by the current sensing and testing technologies, it is challenging to directly measure the core temperature of the lithium-ion battery. Furthermore, due to the time-varying convection coefficient and the limited on-board computational resource, it is difficult to accurately estimate the battery core temperature in real-time. Consequently, this paper proposes a joint estimation method for the convection coefficient and the core temperature of the lithium-ion battery based on an efficient thermal model. Specifically, considering the computational cost and the estimation accuracy, a two-parameter polynomial approximation method is employed to reduce the model order, and the dual extended Kalman filter algorithm is utilized to simultaneously estimate the core temperature and the convection coefficient of the battery. The validation results show that the proposed method can accurately and quickly predict the core temperature under unknown cooling conditions, and the root mean square error is less than 1°C.

Compared to conventional means of transport thatuse fossil fuels, electric vehicles are known to reduce pollution levels as they take power from renewable sources of energy stored in energy storage devices like batteries and fuel cells. Core temperature estimation of batteriesis extremely important inbattery management systems for preventing thermal runaway and ensuring safe operation. In this study, core temperature is estimated using a Kalman filter for two different battery chemistries viz; lithium polymer and lithium iron phosphate using a second-order thermal model. Further, a linear regression model is applied to verify the prediction over the trained and tested dataset. The lithium iron phosphate prediction curvehad a fit of approximately 82-83%, whilelithium polymerhad a fit of 72-82% during the charging and discharging of OCV-SOC variation.

Health-conscious battery management systems (BMSs) that rely on surface temperature measurements are insufficient for managing automotive lithium-ion batteries (LIBs). Experimental studies have shown temperature differences of up to <inline-formula> <tex-math notation="LaTeX">$10~^{\circ }$ </tex-math></inline-formula>C between surface and core of cylindrical LIBs. BMSs that consider only surface temperature overlook critical thermal information. The missing monitoring can delay detecting thermal events within the cell, accelerating battery degradation and increasing the risk of thermal runaway. This article introduces two deep learning algorithms to address this: Kolmogorov-Arnold network (KAN) and interconnected long short-term memory (LSTM) network. Both approaches estimate the core temperature of LIBs without requiring surface temperature feedback to the neural network. Experimental validation revealed a core temperature mean absolute error (MAE) of <inline-formula> <tex-math notation="LaTeX">$0.55~^{\circ }$ </tex-math></inline-formula>C with a computational cost of 2.9–3.2 ms for KAN. The proposed interconnected LSTM reached a MAE of <inline-formula> <tex-math notation="LaTeX">$0.80~^{\circ }$ </tex-math></inline-formula>C. The performance of the two core temperature estimation techniques was further evaluated under dynamic loading profile using urban dynamometer driving schedule (UDDS) drive cycle. The KAN method achieved a MAE of <inline-formula> <tex-math notation="LaTeX">$0.325~^{\circ }$ </tex-math></inline-formula>C, demonstrating its adaptability to dynamic operating conditions. The two proposed methods, primarily KAN, are both adaptive and computationally efficient, making them suitable for integrating onboard BMS and cloud-enabled digital-twin-based BMS systems.

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Reliable estimation of the state of charge (SoC) and core temperature (CoT) of battery cells is paramount for formulating efficient energy and thermal management strategies. Focusing on cylindrical Li-ion batteries, this article constructs an equivalent circuit model and a two-state thermal model; then these two different-physics lumped-mass models are close-looped using bridge variables encompassing temperature, heat, and SoC. Notably, in addition to the conventional irreversible thermogenesis of ohmic effect, the generally ignored reversible entropy heat is modeled and experimentally calibrated as well. Then, both the electrical and thermal model parameters are adaptively identified using the variable forgetting factor least square algorithm. Finally, a computationally efficient and nonlinearity-compatible algorithm, namely the singular value decomposition-based Kalman filter, is utilized for the joint estimation of SoC and CoT. Experimental validations under dynamic load excitations demonstrate the robustness and accuracy of the designed scheme, achieving favorable performance with errors as low as 5% for SoC and 0.2 °C for CoT.

Excessive core temperature in lithium-ion batteries for new energy vehicles can accelerate electrochemical corrosion, thereby degrading battery lifespan. In extreme cases, it may even induce thermal runaway. However, the inherent complexity of internal electrochemical reactions and the battery’s sealed structure make direct measurement of its core temperature highly challenging. To address the challenge in precise core temperature measurement, this paper proposes a maximum correntropy criterion improved adaptive extended Kalman filter (MCC-AEKF) for accurate battery core temperature estimation. The method establishes a battery thermal model with parameters identified by adaptive forgetting factor recursive least squares, then enhances the traditional EKF by incorporating MCC and Sage-Husa adaptive criterion to mitigate the effects of non-Gaussian noise and initial parameter settings, thereby improving estimation accuracy. Validation through co-simulations in AMESim and MATLAB/Simulink under urban dynamometer driving schedule and highway fuel economy test conditions demonstrates that the proposed MCC-AEKF achieves at least 41.7% higher accuracy than conventional methods. This approach effectively resolves the low-accuracy issue in traditional algorithms for core temperature estimation of new energy vehicle power batteries, significantly enhancing battery safety.

Accurate temperature estimation is crucial for safety and increased lifespan for lithium-ion batteries (LIBs) batteries. LIBs surface and core temperatures can differentiate by up to 10°C under dynamic current loadings. Considering only surface temperature for battery management contributes to battery degradation and may result in thermal runaway. Therefore, this paper introduces a Physics Informed Neural Network (PINN) utilizing Kolmogorov-Arnold Network (KAN) to estimate surface and core temperature and compares the results with a Feedforward Neural Network and a Long Short-Therm Memory (LSTM) network. The experimental validation at CC-CV and dynamic conditions demonstrated a mean absolute error (MAE) of 0.752 °C and 0.824 °C for core and surface temperature, respectively, through CC-CV cycles at a broad range of ambient temperatures. While PINN generally demonstrates the potential for accurately estimating the core and surface temperatures of LIBs, KAN exhibits lower accuracies compared to the LSTM-PINN (0.644 °C / 0.454 °C) and FNN-PINN (0.761 °C / 0.475 °C) models.

With the wide application of lithium-ion batteries (LIBs), its safety has attracted much attention. Due to the limitations of existing sensors and measurement technologies, the internal temperature of LIBs cannot be measured directly, which makes it impossible to monitor the core temperature of LIBs in real time. This will cause hidden hazards to the safe use of LIBs. In this paper, the accurate battery heat generation model is established by combining the heat generation model proposed by Bernardi with the heat transfer and heat dissipation model. Particle swarm optimization (PSO) algorithm is used to identify the parameters of the lumped parameter two-state thermal model of LIBs proposed in this paper. In the experiment, after drilling the battery, the built-in temperature sensor is utilized to measure the real core temperature, and then the unscented Kalman filter (UKF) algorithm is employed to estimate the core temperature. The experimental results show that the estimation errors by the method used in this paper are small and have good adaptability and robustness, which provides a reliable method for core temperature monitoring of LIBs.

Estimating the core temperature of the battery is not only an important task of the battery management system, but also a key means to ensure the safety and reliability of the battery for other important purposes. The core temperature of the battery cannot be observed directly, but it has a certain correlation with other battery measurable parameters (current, voltage, ambient temperature, surface temperature). Therefore, this paper proposes an iteration method based on an improved recurrent neural network algorithm (RNN) whose name is simple recurrent units (SRU) to calculate this correlation, and then estimates the core temperature of the battery under high dynamic driving condition. The experimental results show that this method can accurately estimate the temperature of lithium-ion battery cell of electric vehicle under wide ambient temperature, and mean square error is than 0.604566.

In the battery thermal management system, temperature is a core element, and accurate temperature acquisition directly affects system reliability. In response to the problem that sensor temperature measurement is easily affected by local deviations and the estimation accuracy is insufficient, this paper proposes a surface and core temperature fusion estimation method based on a thermal-electric coupling model. A thermal-electric coupling system is constructed by a second-order RC circuit and a lumped parameter thermal model to obtain the surface and core temperatures of the battery, and a weighted fusion strategy is used to improve the estimation accuracy and provide more reliable input for cooling control. Simulation verification based on typical working conditions shows that this method can achieve high-precision temperature estimation under various conditions, has good dynamic response and robustness, and provides theoretical support and data basis for the optimization of battery thermal management strategies.

Lithium ion (Li-ion) batteries in electric vehicle (EV) applications must operate within a narrow temperature range to ensure safety, performance and longevity. Hence, advanced thermal management strategies should have access to internal cell temperatures in a battery pack. In real world application, surface temperatures can be measured, but it is difficult to place a sensor at the core (which can be more than 10°C higher that the surface) due to the added cost and intrusive nature.In this paper, a pack level thermal model is developed for a cylindrical cell battery module which is modular and scalable. This model is used in a Kalman filter based Thermal State Observer (TSO) which is constructed to be real-time capable for application in a Battery Management System (BMS). The TSO uses limited cell surface measurements to estimate the core temperature of the full battery pack. The paper also discusses the methodology for characterization and validation of the thermal model and TSO.

No abstract available

Relevance. Currently, global warming represents one of the most pressing environmental challenges, requiring immediate action. One of the key strategies for mitigating anthropogenic impact on the climate is the transition to renewable energy sources. However, their intermittent nature (dependence on sunlight, wind, and other factors) necessitates the use of efficient energy storage systems. Moreover, in resource exploitation, energy storage systems may be required as an auxiliary source of electrical energy in critical situations. In this context, lithium-ion batteries have gained particular importance as efficient energy storage devices due to a number of inherent advantages. However, the widespread deployment of lithium-ion batteries is hindered by a critical safety issue – thermal runaway. Therefore, thermal state monitoring of lithium-ion batteries plays a crucial role in ensuring safe operation and extending service life. Aim. To develop an algorithm for estimating the internal electrochemical temperature of lithium-ion batteries based on external sensors mounted on the battery surface. Methods. The experimental data were collected and analyzed using mathematical and numerical methods for parameter calculation. Results and conclusions. The study demonstrates that during charging, the maximum absolute estimation error does not exceed 0.85°C, while during discharging it remains below 3.1°C. The obtained results indicate that the proposed algorithm provides sufficiently accurate estimation of internal lithium-ion battery temperature based on surface temperature and voltage measurements. 

This paper presents a core temperature estimation scheme for LIBs under internal thermal faults. First, a model-based incipient internal fault detection scheme is proposed using the SOH-coupled electro-thermal-aging model of the LIB. A nonlinear observer estimates the states and parameters (internal resistance) of the SOH-coupled state space model and generates multiple residuals, such as output voltage and surface temperature. Second, an adaptive threshold is designed to detect convective cooling and internal thermal resistance faults. The adaptive threshold minimizes the false positives due to the battery’s health degradation and model uncertainties. Finally, a second neural network (NN)-based observer is proposed to learn the fault dynamics and estimate the core temperature under fault conditions. Analytical and numerical results are presented to show the convergence of the state and NN weight estimation errors.

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State of charge (SOC) estimation and thermal management are the key components of electric vehicle (EV) management systems (BMSs). However, accurate estimation is challenging, and battery temperature has a great impact on SOC estimation and battery thermal management. To address these challenges, the proposed model integrates the equivalent circuit model (ECM) and thermal dynamic equations. This model can accurately estimate SOC, terminal voltage, surface and core temperatures, and internal resistance of Li-ion batteries. Experiments are conducted using a battery cell under the Hybrid Pulse Power Characterization (HPPC) test method and a Fiat 500e 2020 electric vehicle battery pack under the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) signals. The experimental results demonstrate that the proposed model achieves an SOC estimation error of less than 1%. Additionally, the model can provide an estimate of internal resistance and core temperature, which can be utilized in state of health (SOH) estimation and thermal management. The application of the proposed model can significantly enhance battery safety, efficiency, and extend the life of EV batteries.

The onboard battery self-heaters are employed to improve the performance and lifetime of the automotive lithium-ion batteries under cold climates. The battery performance is determined by the core temperature which is significantly higher than the surface temperature during the fast self-heating, while only the surface temperature can be directly measured. By estimating the core temperature to monitor the self-heating condition, the heating time and the energy consumption can be improved. However, the high-frequency heating current and the time-variant battery impedance cannot be measured in real time by a low-sampling-rate battery management system, so that the regular core temperature estimation methods are not applicable during the self-heating. To solve the issues, an online core temperature estimation algorithm based on the lumped thermal–electrical model is developed for the onboard ac self-heater. By implementing an extended state observer to compensate for the effect of the parameter uncertainties, the core temperature can be accurately detected even with the unknown internal resistance and root mean square (RMS) heating current. The experimental validation of 18 650 lithium-ion batteries shows that the core temperature estimation error is within only 1.2 °C. As a result, the self-heating time and energy consumption can be reduced by 50%.

Batteries store chemical energy into electrical energy, making them crucial to clean energy systems, especially in hybrid and electric vehicles. For this application, a cylindrical LiNiMnCoO2 lithium-ion battery is popular. Temperature, material composition, current draw, and charge cycles affect battery performance. The study proposes a simulation-based approach for predicting internal battery temperature by analyzing temperature fluctuations observed during the discharging levels. For case studies, the battery had a capacity of 3.5 Ah and was tested at discharge levels of 0.5 C, 1 C, and 1.5 C. The results demonstrated stable thermal properties within the battery system. Moreover, the graph from natural convection studies decisively illustrated that the surrounding environmental temperature significantly impacts thermal measurements. This emphasizes the importance of environmental factors in battery performance and thermal management. Mesh-independent test profiles agreed with observed temperature values at 1 C. Mesh characteristics were obtained for each mesh element, providing confidence that is comparable to experimental results. Under insulated conditions, error margins were 2.71% at 0.5°C discharge, 2.1% at 1°C, and 1.77% at 1.5°C. The core internal battery's predicted thermal characteristics indicated the highest temperature. The safe operating temperature range for the core internal temperature of the LiNiMnCoO2 battery is 30°C to 45°C.

Temperature monitoring is critical for safe operation and optimal performance of lithium-ion batteries. While surface temperature can be measured directly using external sensors, it lags behind the core temperature, which more accurately reflects the thermal state of the battery. In this work, we propose a physics-informed neural network (PINN) framework to estimate the core temperature by leveraging experimentally measured voltage, current, and temperature data. The approach combines a CNN-MLP based network with residuals from a lumped heat transfer model, forming a hybrid loss function to predict the battery surface temperature. To improve stability, a sequential tuning strategy is adopted for the physics-based and the neural network parameters. A correlation learned between the electrical and thermal resistances is then used to infer the core temperature from the predicted surface temperature. Results show that incorporating physics-based residuals into the network training significantly enhances prediction accuracy, particularly under data scarce conditions where purely data-driven model fails. Compared to the purely data-driven model with a mean absolute percentage error of 23.16% for surface temperature estimation, the proposed PINN achieves only 2.3% error, for generalization testing. Because the physical parameters are derived from the measured data, the framework is adaptable across different cell chemistries.

Lithium batteries receive widespread attention as core components in electric vehicles, with their performance being significantly influenced by temperature. To enable accurate online estimation of battery temperature, this article proposes a self-adaptive 3-D thermal modeling method. The model's self-adaptation is achieved through a two-step resistance transfer algorithm (RTA). First, a linear relationship between temperature and battery resistance is established based on the Arrhenius equation. This relationship is used to calibrate the migration coefficient from the reference battery resistance to the target battery resistance. Second, the heat generation model of the target battery is updated based on this migration coefficient to achieve thermal model self-adaptation. For precise online temperature estimation, a 3-D thermal conduction equation is solved in place of a lumped parameter model, and a thermal resistance network is developed to simplify the equation and expedite the solution process. This network divides the battery into microstructures and refines the heat transfer relationships of these microstructures using the first law of thermodynamics. Based on these models, we propose a mechanism-data-driven self-adaptive algorithm to accurately compute the battery's 3-D temperature distribution online. Testing on different batteries shows that RTA achieves accurate resistance transfer with a maximum error below 0.0341 mΩ, whereas the online thermal model estimates temperature distribution with a computation time of 0.496 s and an error below 1.515 °C. Additionally, the comparison results demonstrate that this method (0.496 s) is significantly more efficient than the finite element method (2662.33 s) in terms of computation time.

No abstract available

The State of Charge (SOC) and thermal conditions of lithium batteries are essential factors in the Battery Management System (BMS). Precise assessment of the SOC and core temperature of lithium batteries is crucial for the development of the BMS. This study utilizes the Square Root Cubature Kalman Filter (SRCKF) method along with the electro-thermal coupled model of lithium batteries to achieve accurate estimations of the battery’s SOC and core temperature. Initially, this research determines the parameters of the electro-thermal coupled model using the Forgetting Factor Recursive Least Squares method and the Hybrid Pulse Power Characterization tests, establishing the lithium battery’s electro-thermal coupled model. In order to validate the accuracy of SRCKF estimates, simulations were carried out under conditions defined by the Urban Dynamometer Driving Schedule, comparing the accuracy of its estimations with those of the Extended Kalman Filter and the Unscented Kalman Filter under identical conditions. The simulation outcomes demonstrate that the SRCKF can precisely estimate the battery’s SOC and core temperature, thus effectively meeting the requirements of the BMS in practical application scenarios. This study utilizes the open-source experimental dataset of the LG18650HG2 lithium battery.

Fast charging is one of the main requirements and challenges for electric vehicle batteries. Currently, common charging profiles utilize an open-loop control, which relies on a priori knowledge. It's necessary to use a closed-loop charging technique, where the charging current is controlled by real-time voltage and temperature, particularly when high charging current. Moreover, the massive difference between surface and core temperature leads to thermal issues. Therefore, this paper proposes a closed-loop fast charging strategy (CFCS) based on core temperature control for lithium-ion batteries (LIBs), with an awareness of thermal safety. CFCS includes three modes, i.e., pulse current charging (PCC) mode, constant temperature (CT) mode with a proportional-integral-derivative (PID) controller, and constant voltage (CV) mode. Besides, an extended state observer (ESO) is applied for real-time core temperature estimation, combined with a two-state thermal model. Based on the core temperature control, there is a 40% reduction in charging time compared to the previous method. Meanwhile, core temperature is maintained in a safe range, which keeps the LIB from thermal runaway. The experimental results show the proposed strategy can balance rapidity and security, with a wide application range and strong robustness.

Driven by increasingly stringent carbon emission regulations from the International Maritime Organization (IMO), the maritime industry increasingly requires eco-friendly power systems and enhanced energy efficiency. Lithium-ion batteries, a core component of these systems, necessitate precise temperature management to ensure safety, performance, and longevity, especially under high-temperature conditions owing to the inherent risk of thermal runaway. This study proposes a sensorless temperature estimation method using a long short-term memory network. Using key parameters, including state of charge, voltage, current, C-rate, and depth of discharge, a MATLAB-based analysis program was developed to model battery dynamics. The proposed method enables real-time internal temperature estimation without physical sensors, demonstrating improved accuracy via data-driven learning. Operational data from the training vessel Hannara were used to develop an integrated organic Rankine cycle–energy storage system model, analyze factors influencing battery temperature, and inform optimized battery operation strategies. The results highlight the potential of the proposed method to enhance the safety and efficiency of shipboard battery systems, thereby contributing to the achievement of the IMO’s carbon reduction goals.

In this paper, results of a simulation carried out to estimate the core temperature (Tc) of a Lithium ion (Li) battery for various C rates and a standard drive cycle FTP75 using MATLAB / Simulink are presented. A mathematical model of a charger was developed by integrating a SEPIC with a Li ion battery. The SEPIC was modeled using governing volt sec and amp second balance dynamic equations and was supplied to the battery of nominal capacity 40Ah. A thermal model of the battery was developed to investigate Tc, based on measured ambient (Tamb) and surface (Ts) temperatures. It was found Tc increased during the discharge process and the difference between Tc and Ts increased to large values as the C rate increased. With the proper estimation of Tc, efficient thermal management can be achieved. Hence, the State of Health (SOH) for a battery during fast discharging and charging can be monitored effectively, thus enabling development of an efficient and safe Battery Management System.

Operation above acceptable limits in terms of current, voltage, and temperature can lead to lithium batteries overheating, increasing the risk of thermal runaway, which can also degrade battery materials more quickly, reducing overall lifespan. Estimating the state of power (SOP) of a battery is necessary for battery safety control and preventing operation above acceptable limits. However, the SOP is influenced by coupled multiple parameters including the state of charge, state of health, and core temperature, which make it challenging to estimate comprehensively. Based on the electro-thermal model, this study proposes a multi-parameter coupled method for comprehensively estimating the SOP considering the core temperature. This method provides a robust approach to accurately assessing the SOP across varying core temperatures, states of charge (SoC), and voltage levels. The combination of maximum likelihood estimation, adaptive genetic algorithms for parameter identification, and the unscented Kalman filter for state estimation was found to enhance the accuracy and robustness of battery models. The results show that the battery core temperature and terminal voltage are important and the main limitation on the SOP, respectively. This study lays a strong foundation for effective energy management and life extension of lithium batteries, particularly in high-temperature environments.

Lithium-ion cells are widely used in various applications. For optimal performance and safety, it is crucial to have accurate knowledge of the temperature of each cell. However, determining the temperature for individual cells is challenging as the core temperature may significantly differ from the surface temperature, leading to the need for further research in this field. This study presents the first sensorless temperature estimation method for determining the core temperature of each cell within a battery module. The accuracy of temperature estimation is in the range of ΔT≈1 K. The cell temperature is determined using an artificial neural network (ANN) based on electrochemical impedance spectroscopy (EIS) data. Additionally, by optimizing the frequency range, the number of measurement points, input neurons, measurement time, and computational effort are significantly reduced, while maintaining or even improving the accuracy of temperature estimation. The required time for the EIS measurement can be reduced to 0.5 s, and the temperature calculation takes place within a few milliseconds. The setup consists of cylindrical 18,650 lithium-ion cells assembled into modules with a 3s2p configuration. The core temperature of the cells was measured using sensors placed inside each cell. For the EIS measurement, alternating current excitation was applied across the entire module, and voltage was measured individually for each cell. Various State of Charge (SoC), ambient temperatures, and DC loads were investigated. Compared to other methods for temperature determination, the advantages of the presented study lie in the simplicity of the approach. Only one impedance chip per module is required as additional hardware to apply the AC current. The ANN consists of a simple feedforward network with only one layer in the hidden layer, resulting in minimal computational effort, making this approach attractive for real-world applications.

Energy optimization in Hybrid Electric Vehicles (HEVs) relies on the instantaneous battery pack capacity and power limits which can be impacted by a single degraded cell. Further, often battery cooling by a single fan induces a temperature gradient on individual cells that may cause a differential degradation among them. Strategies for cell balancing need to use not only the estimate of State of Charge (SOC) but also estimate of the core temperature of each cell. Here an Unscented Kalman Filter (UKF) based SOC estimator is designed using an electrical equivalent circuit model of lithium ion cell where the model parameters vary with SOC, core temperature and charge-discharge modes. These model parameters are obtained from pulsed charge and discharge test done on the cell. Outputs of the UKF based estimator, which are SOC and polarization voltage, are fed as inputs to a cell core temperature estimator. Core temperature of cells can be estimated from its surface temperature and electrical cell model. However, only a limited number of thermistors can be put inside the battery pack which makes it difficult to measure surface temperature of each cell. In that case it is required to know the temperature gradient inside the pack which will be used to estimate the core temperature of all the cells. The data used for this work is obtained from NASA Prognostic Data Repository.

The Battery Management System plays a critical role in ensuring the longevity, safety, and optimal performance of batteries by performing state of charge and health estimation, thermal management, cell balancing, and charge control. Thermal management is a crucial component that is responsible for temperature monitoring and control, managing heat generation and dissipation, preventing thermal runaway, and optimizing battery performance. This paper includes several original contributions. (1) A four-state lumped thermal model is introduced to model the core and surface temperatures of the battery. (2) Accordingly, various characterization tests were conducted on a lithium-ion Prismatic battery to log the thermal behavior of the battery. The third-order Equivalent Circuit Model is used to calculate the generated heat inside the cell using the measured physical parameters such as voltage, and current. (3) Machine learning methods like Particle Swarm Optimization and Genetic Algorithm are used and compared to determine the parameters of the thermal model. (4) A novel, reliable 3rd order Smooth Variable Structure Filter is suggested in this work and evaluated against the Extended Kalman Filter, SVSF, and 2nd-order SVSF. The proposed strategy demonstrated higher accuracy compared to the abovementioned filters.

No abstract available

The increasing electrification of large‐scale industrial equipment, such as heavy‐duty electric mining trucks, necessitates precise state‐of‐charge (SOC) estimation for lithium‐ion batteries under high‐rate operations. This is challenging due to the significant electro‐thermal coupling effect at high discharge rates. This study introduces a novel SOC estimation method that incorporates electro‐thermal coupling to enhance accuracy and robustness. An electrochemical‐thermal coupling model is developed to capture interactions between electrochemical reactions and internal heat generation. Subsequently, a reduced‐order electro‐thermal coupling model is formulated to enable real‐time co‐estimation of SOC and internal temperature. An electro‐thermal SOC estimator based on the Extended Kalman Filter (EKF) is then designed. The proposed method's performance is validated using diverse test profiles with varying initial SOC values. Experimental results show exceptional accuracy and robustness, with a mean absolute error of 3.044% and a root mean square error of 4.658% in the challenging 15 C high‐rate pulse discharge test, despite a 40% initial SOC error. This approach significantly outperforms the conventional EKF‐only method, offering improved SOC estimation accuracy for high‐rate applications.

Aiming at the current lithium-ion battery storage power station model, which cannot effectively reflect the battery characteristics, a proposed electro-thermal coupling modeling method for storage power stations considers the characteristics of the battery body by combining the equivalent circuit model and accounting for the effect of temperature on the battery. Based on the modeling of a single lithium-ion battery, the equivalent circuit model and thermal model are integrated to create the battery’s electro-thermal coupling model. The parameters of this coupling model are determined using the particle swarm algorithm. On this basis, the battery compartment model of the energy storage station is analyzed and verified by utilizing the circuit series–parallel connection characteristics. Subsequently, the electro-thermal coupling model of the energy storage station is established. The dual Kalman filter algorithm is utilized to simulate and validate the electric–thermal coupling model of the energy storage power station, considering ontological factors such as battery voltage, current, and temperature. The results demonstrate that the established coupling model can accurately determine the SOC and temperature of the power station. This ability allows for a more precise reflection of the battery characteristics of the energy storage station. It also validates the accuracy and effectiveness of the electric–thermal coupling model of the energy storage station. This finding is crucial for assessing the state and ensuring the safe operation of the battery system in the energy storage station.

To address the inadequacy of existing battery storage station models in reflecting battery characteristics, a novel method is proposed for modeling an energy storage station with battery thermal coupling. This approach is based on a single lithium-ion battery model, where an equivalent circuit model and an equivalent thermal model are developed. These two models are then coupled to form a battery electro-thermal coupling model. Building upon this foundation, a method of equivalent representation is employed to derive an equivalent model for the storage plant, known as the electro-thermal coupled energy storage station model. Under the US06 composite cycle operating condition, the model takes into account the battery's inherent properties such as capacity, voltage, and temperature. The model's accuracy and applicability are assessed using the Double Kalman Filter Algorithm (D-EKF) for validation. The simulation results demonstrate that the proposed coupled model effectively captures the state of charge (SOC) and core temperature of the plant with high precision. This method holds significant theoretical and technical implications for the development of large-scale energy storage facilities, providing a solid foundation for future advancements. facilities.

Owing to the nonnegligible impacts of temperature on the safety, performance, and lifespan of lithium-ion batteries, it is essential to regulate battery temperature to an optimal range. Temperature monitoring plays a fundamental role in battery thermal management, yet it is still challenged by limited onboard temperature sensors, particularly in large-scale battery applications. As such, developing sensorless temperature estimation is of paramount importance to acquiring the temperature information of each cell in a battery system. This article proposes an estimation approach to obtain the cell temperature by taking advantage of the electrothermal coupling effect of batteries. An electrothermal coupled model, which captures the interactions between the electrical and the thermal dynamics, is established, parameterized, and experimentally validated. A closed-loop observer is then designed based on this coupled model and the extended Kalman filter to estimate the battery temperature by merely using the voltage measurement as feedback. The electrothermal coupling effect enables the full observability of batteries’ internal states from their voltage, and contributes to an accurate and robust temperature estimation. The capability of the proposed estimation method has been demonstrated via experiments, with root-mean-square error less than 0.7 °C in various scenarios.

Accurate and timely estimation of a lithium battery's status during operation is essential for ensuring both safety and performance. Traditional estimation methods typically rely on individual parameters such as voltage, current, or temperature, making it difficult to comprehensively assess the battery's overall safety. In this paper, we propose a voltagetemperature co-estimation method based on the Extended Kalman Filter (EKF). Utilize the least squares method to perform battery parameter fitting, and establish a second-order RC model as well as an electro-thermal coupling model. By developing the two models, this approach enables the simultaneous prediction of voltage and temperature. The feasibility of the proposed method is validated using battery data from the University of WisconsinMadison. The RMSE values for voltage and temperature predictions were 0.061 V and $0.0994^{\circ} \mathrm{C}$ respectively. The estimated results provide a valuable reference for battery safety assessment, enabling the early and comprehensive detection of potential safety hazards.

This paper presents a novel application of model predictive control (MPC) to the problem of managing lithiumion cell performance using a highly accurate low-order electrothermal equivalent circuit model and is experimentally validated via laboratory experiments. The proposed method uses MPC to ensure compliance with cell-level operational limits and has the potential to extend lifetime by mitigating certain mechanisms of cell degradation leading to capacity fade. A five-state electrothermal model is developed, characterized and validated. Implementation employs an extended nonlinear Kalman filter for state estimation and MPC for controlling charge/discharge current. The complete method is experimentally validated using a 26650 cylindrical format lithium-iron phosphate (LFP) cell. The new method: (i) develops a fully coupled electro-thermal model of cell dynamics; (ii) incorporates a dynamic hysteresis model to improve accuracy; (iii) employs a nonlinear Kalman filter for accurate state estimation to inform the MPC algorithm; and (iv) utilizes a modified form of MPC which correctly models direct feed-through behavior to characterize ohmic resistance.

This paper proposes a novel thermal fault diagnosis method of lithium-ion battery where Extended Kalman filter (EKF) has been applied. Thermal fault generally occurs due to sudden heat generation in the core or internal parameter variation of the battery. As a result, core temperature as well as surface temperature of the battery has been changed. But it is very difficult to measure battery core temperature directly, so EKF is used to estimate core as well as surface temperature of the battery accurately. To implement EKF, an electro-thermal discretized model of cylindrical lithium-ion battery cell is developed where estimated data by EKF is compared with the measured data. The residual signal is generated which is the difference between the measured and the estimated temperature from battery. Under normal operating condition, the residual signal does not indicate zero mean value, but when thermal fault occurs, residual signal shows non-zero mean value indicating the occurrences of fault. Finally, battery performance is tested under noisy environment by changing variance of the noisy data, and EKF diagnose the thermal fault effectively compared to previous methods.

Lithium-ion batteries are widely used in fields such as new power systems. Accurate prediction of battery temperature is crucial for the effective design of thermal management systems and the management of battery thermal runaway. This paper proposes a temperature prediction algorithm based on a model and a multi-step extended Kalman filter (EKF) algorithm. Firstly, an electrochemical-thermal coupled model is constructed by combining the SP+ model with a lumped parameter thermal model. Then, model parameters are obtained using the excitation-response method. Finally, the model is embedded into the multi-step EKF algorithm, using the entropy coefficient as the state variable, to achieve accurate temperature prediction. Experimental results show that under 1C constant current discharge conditions and typical frequency regulation conditions of energy storage, the mean absolute error of the temperature prediction is within 0.9K.

This paper proposes a variable parameter lumped thermal model to accurately characterize thermal behavior of lithium-ion batteries under different environment temperatures. To solve the issue of model parameter identification, the Gravitational Search Algorithm (GSA) is introduced, and the Kalman Filter (KF) algorithm is adopted to filter out process noise and observation noise. Temperature estimation simulations for batteries under two different environment temperatures are conducted, achieving accurate temperature estimation of the batteries. Experimental results show that the GSA-KF algorithm has high estimation accuracy and small error for the lumped parameter thermal model. The GSA-KF algorithm provides an effective method for lithium battery thermal estimation.

Accurate state of temperature (SOT) estimation for lithium-ion battery is essential to guarantee the safety and long-term stable operation of electric vehicles. While the majority of current physical modeling techniques rely on various types of equivalent circuit models (ECM), challenges persist in accurately estimating with the electrochemical models. Therefore, this paper proposes a methodology for temperature estimation based on a restructured electrochemical-thermal coupling model, and employing the Adaptive Unscented Kalman Filter (AUKF) algorithm to enhance battery SOT estimation accuracy. This method initially establishes a Thermal Single Particle Model (TSPM) that integrates a Single Particle Model (SPM) with a Lumped Thermal Model (LTM). And the model's alignment with experimental data further reinforced the thermal model's precision. Then, to account for the impact of noise on computational accuracy, the AUKF algorithm is introduced to adaptively process noise and filter the temperature values by the model. Finally, the validation of the algorithm is conducted through a comparative analysis with the temperature predictions of an open-loop model. The results indicate that the reconstructed electrochemical-thermal coupling model demonstrates high effectiveness in battery temperature estimation. By integrating the AUKF, the accuracy of temperature predictions was significantly enhanced, with the temperature prediction error notably reduced from 0.28°C to 0.07°C, achieving a 61.74% improvement in estimation accuracy. This paper contributes to the research on optimizing the SOT estimation methods for lithium batteries.

The internal battery parameters of the lithium-ion battery (LIB) energy storage system may be inconsistent due to different aging degrees during the operation, and the thermal effect can also threaten the safety of the system. In this paper, based on the second-order resistor-capacitor (2-RC) equivalent circuit model (ECM) and the dual extended Kalman filter (DEKF) algorithm, an electrical simulation model of a LIB pack with inconsistent parameters considering the thermal effect is established, in which state of charge (SOC) and state of health (SOH) are estimated using DEKF while the temperature is calculated by a thermal module. The simulation results show that the DEKF algorithm has a good effect on battery state and parameter estimation, with the root mean square error (RMSE) of voltage is lower than 0.01 V and SOC mean average error (MAE) is below 1.50 % while SOH error is 3.37 %. In addition, the thermal module can provide an accurate estimation on the inconsistent temperature rise of the battery pack, and the MAE between the model-calculated temperature and the experiment is no more than 6.60 %. This paper provides the basic data for the scale-up of the electrothermal co-simulation model of the LIB energy storage system.

To address the challenge of directly and accurately measuring the internal temperature of lithium‐ion power batteries in electric vehicles, this paper proposes an online precise estimation method for battery internal temperature based on the Aquila Optimizer‐optimized Adaptive Strong Tracking Extended Kalman Filter (AO‐ASTEKF). Building on a battery equivalent thermal model with parameters identified using the Genetic Algorithm (GA), the Aquila Optimizer (AO) is employed to optimize the initial noise covariance settings of the traditional Extended Kalman Filter (EKF), thereby mitigating the impact of improper initialization. To resolve the estimation deviation caused by fixed noise covariance in EKF, the Sage‐Husa adaptive filtering technique is introduced to enable adaptive adjustment of noise covariance values. Furthermore, to counteract the estimation accuracy degradation of the filter due to sudden temperature changes in high‐temperature environments, the Strong Tracking (ST) filter is incorporated to enhance the tracking capability of the EKF. Through co‐simulation in AMESim and MATLAB/Simulink, the accuracy of the proposed AO‐ASTEKF algorithm in estimating battery internal temperature is validated under different ambient temperatures and operating conditions. Experimental results demonstrate that the AO‐ASTEKF algorithm improves estimation accuracy by at least 58.46% compared to both the traditional EKF and the Strong Tracking Extended Kalman Filter (STEKF). This method effectively overcomes the limitations of conventional algorithms in accurately estimating battery internal temperature, holding significant importance for ensuring battery safety and enhancing battery performance.

Lithium-ion batteries are extensively utilized in energy storage systems due to their relatively high output voltage, long cycle life, and high energy density. The integration of digital twin technology within battery management systems (BMS) enables the prediction of battery performance under varying scenarios. Accurate estimation of the State of Charge (SOC) and State of Temperature (SOT) remains a significant technical challenge in battery state estimation. To address the challenges of model uncertainty and estimation inaccuracies in lithium-ion batteries during operation, this paper proposes a novel method for battery parameter identification and state estimation based on a digital twin framework. Firstly, a digital twin architecture for lithium-ion batteries is designed. A coupled electro-thermal model is established. Secondly, the FFRLS method in proposed online to identify thermal parameters in the scenario that internal battery temperature are unavailable. Then, a Q-AUKF algorithm is proposed to address divergence in Kalman filtering and improve SOC and SOT accuracy. Finally, the developed digital twin battery model and the proposed algorithm are validated through experiments.

Abstract This paper investigates the state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200 s despite a 30% error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.

Temperature estimation is crucial in a battery thermal management system that ensures the safe operation of the battery pack. However, the current method of collecting temperature by temper-赵文文

The charging rate of lithium-ion batteries (LIBs) constitutes an essential metric for quantifying the competency of electric vehicles (EVs) and energy storage systems (ESSs) in restoring power expeditiously. Nevertheless, unrestricted escalation of the charging current may trigger hazardous thermal runaways in battery packs. Hence, this work is concerned with optimizing the battery charging strategy from a thermal safety perspective. Instead of relying on the conventional thermal-coupling equivalent circuit models, a numerical approach based on a thermal-coupling simplified electrochemical model (TC-SEM) is proposed to predict the battery voltage and temperature via recursion. The potential error accumulation in the recursive process is suppressed by a multistep-ahead Kalman filter, which operates in concert with measurable terminal voltage and temperature. Subsequently, the aforementioned prediction algorithm is integrated into a model predictive control (MPC) framework. Central to the MPC framework is a liquid cooling system that seeks to regulate the battery temperature, and thus the efficacy of the prediction algorithm should be, and in fact is, verified in terms of the temperature control ability of an actual cooling system. Experimental result shows that, during the battery charging process, the maximum temperature only overshoots the prescribed temperature by 0.1 °C, whereas the average error is just −0.08 °C, which empirically validates the proposal.

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Unmanned Aerial Vehicles (UAVs) are a promising application to deal with diverse industrial and social problems. In order to increase the utilization and reliability of UAVs, batteries play a big role. The flight feasibility evaluation of UAVs should be done in terms of battery before starting the flight missions. The properties of batteries are sensitive to temperature since they generate power through an electrochemical reaction. In this paper, a battery temperature estimator is presented for a system-level UAV flight evaluation considering the usability of end-users. The proposed estimator consists of flight history-aware data preprocessing and a deep neural network-based model instead of the conventional physics-based approach that requires in-depth theories. The flight data is collected through the actual flight experiments of a UAV for training and validation. The proposed method achieves a temperature estimation error of less than $2.02^{\circ}\mathrm{C}$ compared with the actual measured data of a UAV battery. The effectiveness of the proposed estimator is presented by case studies.

Battery packs develop faults over time, many of which are difficult to detect early. For instance, cooling system blockages raises temperatures but may not trigger alerts until protection limits are exceeded. This work presents a model-based method for early thermal fault detection and identification in battery packs. By comparing measured and estimated temperatures, the method identifies faults including failed sensors, coolant pump malfunctions, and flow blockages. The core is a high-accuracy temperature estimation model, integrating a physics-based thermal model with a neural network, achieves a root mean square error of 0.39 °C and a maximum error of 1 °C under a US06 discharge and 6C charge at 15 °C. Tested on a 72-cell air-cooled pack, the method detects faults using only eight temperature sensors within 13 to 45 minutes, with zero false detections in 11 testing cycles. This approach enables early fault alerts, enhancing reliability and safety in electric vehicles. Mina Naguib and colleagues propose an integrated physicsand machine-learning-based method for early thermal fault detection in battery packs. This approach enhances reliability and safety by identifying faults such as sensor failures and cooling system issues before they become critical.

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Temperature plays a significant role in the safety, performance, and lifetime of lithium-ion batteries (LIBs). Therefore, monitoring battery temperature becomes one of the fundamental tasks for the safe and efficient operation of LIBs. Given the limited onboard temperature sensors, this paper proposes a sensorless temperature estimation method suitable for the smart battery system by obtaining the electrochemical impedance of batteries online via bypass actions. A suitable frequency is selected from the battery electrochemical impedance spectroscopy (EIS) to achieve an accurate and robust estimation of the battery temperature through online impedance measurement. Using the battery impedance with this selected frequency, the battery temperature can be estimated under different scenarios, with RMSE less than 1.5 ℃.

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DRT technique offers precise estimation of battery's internal temperature addressing conventional sensor based method for enhanced safety and performance.

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To guarantee safe, efficient, and reliable operations of lithium-ion battery (LIB) systems, it is indispensable to monitor their state of temperature. However, subject to limited onboard temperature sensors and the challenges in measuring battery internal temperature, the directly available temperature information in a battery system is extremely insufficient. To this end, developing sensorless temperature estimation techniques to obtain the temperature of each cell is important. This article proposes an operando impedance-based method to estimate the volume-averaged temperature of LIB in real time under dynamic operating conditions. A generalized rule for selecting optimal impedance parameters has been revealed for the first time through a comprehensive analysis of the electrochemical impedance spectroscopy from different batteries. This rule can greatly reduce the time and effort to select optimal impedance parameters of the target cell for temperature estimations. The selected impedance parameters are then measured intermittently during battery operations via active pulse current injection, which allows the impedance acquisition under both loading and resting conditions. An estimation framework based on long short-term memory recurrent neural network has been proposed by taking advantage of the measured operando impedance, time-series current, and voltage data to achieve real-time temperature estimation, which distinguishes this work from existing impedance-based methods. The proposed methodology has been experimentally validated against different batteries and operating conditions, with the root mean square error of the estimations within 0.46 °C for all cases.

Online temperature monitoring is important for ensuring safe operation of lithium-ion batteries (LIBs). As the battery impedance is related to the internal physical and chemical processes, some efforts have been made to realize sensorless temperature estimation based on the impedance characteristics of LIBs. Unfortunately, the existing impedance-based temperature estimation models are usually derived from pure battery cells, and the effect of peripheral circuit components of systems (e.g., resistors and capacitors) on measured impedance has not been considered. To fill the gap, this article investigates the effect of peripheral circuits (including filter circuits, balancing circuits, and line resistance) on the measured impedances. Taking a ternary lithium battery as a case study, it is found that the imaginary-part impedance at the frequency band of 100 Hz–1 kHz is almost not affected by the peripheral circuits. This can indicate the temperature variation of batteries, and it is independent of state of charge and state of health, which can be chosen as a thermal sensitive electric parameter (TSEP) of batteries. A similar conclusion can also be drawn for a battery with different types and packaging. Based on the obtained TSEP, a single-frequency impedance-based temperature estimation method is presented. Taking a dc/dc converter as a case study, experimental results demonstrate that the estimation method can be integrated into an interface converter for batteries, and the maximum estimation error is less than 5 °C.

The electrochemical reaction in lithium ion power battery is easily affected by temperature, which results in the variation of battery output power and capacity. In order to accurately predict the internal temperature of the battery and provide the basis for the battery management strategy, this paper measured and studied the lithium-ion batteries with different State of Charge (SOC) in a wide temperature range based on the electrochemical impedance spectrum, so as to propose an online estimation method of the internal temperature of the battery based on the electrochemical impedance spectrum. The experimental results show that the imaginary part of the impedance spectrum is not affected by SOC in the range of frequency 10-1000Hz within the range of normal operating temperature of lithium battery (5–55 °C). At the same time, it is sensitive to temperature change and can be used as the characteristic parameter of temperature evaluation. After that, 10Hz is selected as the excitation frequency of the estimation of the internal temperature of the battery, and the internal relationship between the imaginary part value of the battery impedance spectrum and the internal temperature is explored to effectively establish the internal temperature evaluation model of the lithium-ion battery. Finally, the test results show that the temperature evaluation model established in this paper can control the temperature evaluation error within 1.5°C. In this paper, it is proved that the imaginary part of impedance spectrum has a good characterization ability for the battery temperature, which can provide reference for the battery temperature control strategy and improve the temperature rise in the battery working process.

This study presents a method of estimating battery- cell core and surface temperature using a thermal model coupled with electrical impedance measurement, rather than using direct surface temperature measurements. This is advantageous over previous methods of estimating temperature from impedance, which only estimate the average internal temperature. The performance of the method is demonstrated experimentally on a 2.3-Ah lithium-ion iron phosphate cell fitted with surface and core thermocouples for validation. An extended Kalman filter (EKF), consisting of a reduced-order thermal model coupled with current, voltage, and impedance measurements, is shown to accurately predict core and surface temperatures for a current excitation profile based on a vehicle drive cycle. A dual-extended Kalman filter (DEKF) based on the same thermal model and impedance measurement input is capable of estimating the convection coefficient at the cell surface when the latter is unknown. The performance of the DEKF using impedance as the measurement input is comparable to an equivalent dual Kalman filter (DKF) using a conventional surface temperature sensor as measurement input.

The battery digital twin (BDT) is a modern tool that will be used in future intelligent battery management systems (BMS) for Li-Ion batteries (LIB) due to the transition of current technology toward Smart Battery (SB) with information and power processing capability at cell level. The BDT can predict the voltage output based on an impedance model at a given temperature and aging condition and this information can be used for advanced state estimation including sensorless state of temperature (SoT), state of health (SoH) and health management. This paper proposes an online impedance estimation method suitable for the smart battery system which includes a bypass device that can be switched to excite the battery impedance with different frequencies and minimum impact on the load. The performance of the proposed impedance model used in the BDT is compared experimentally in terms of accuracy of the voltage response to dynamic current profiles.

During electric vehicle operation, factors such as battery state-of-charge (SOC) and temperature fluctuate, making accurate temperature diagnosis crucial for effective battery management. This research developed a model for temperature estimation using electrochemical impedance spectroscopy (EIS) to analyze variations in electrochemical properties with temperature. The distribution of relaxation times (DRT) method was applied to extract quantitative indicators. SOC was estimated using an extended Kalman filter (EKF) algorithm, and this information was used to refine EIS-based impedance data for temperature estimation. Experimental data confirmed the sensitivity of these indicators to temperature changes. The final regression model demonstrated improved accuracy and robustness under varying operating conditions.

Online monitoring of Lithium-ion batteries (LIBs) internal temperature (IT) is a mandatory requirement to ensure their safety and longevity. In this article, the second-harmonic current (SHC) that inherently exists in single-phase dc/ac converters is utilized to estimate LIB IT for the first time. First, the SHC needs to be suppressed to the appropriate level as a disturbance signal for online impedance measurement. Then, the dual-channel digital lock-in amplifier is used to calculate LIBs impedance at the second-harmonic frequency (SHF). Moreover, the Pisarenko harmonic decomposition algorithm is adopted to estimate the actual SHF to ensure the accuracy of the impedance calculation. Three commercial 18 650 LIBs are tested at the experimental setup. A strong correlation between the imaginary impedance at SHF and IT is observed, which is nearly not affected by the battery's state of charge. Therefore, an online SHF impedance-based battery IT estimation method is developed. Finally, the validity of the proposed method is confirmed through a comparison between actual and online estimated temperatures.

Battery impedance is an important parameter for estimation of the battery state parameters, such as, state-of-charge (SOC), state-of-health (SOH) and the temperature. However, complexity of the measurement implementation most often prevents wider utilization of the impedance measurement in on-board applications. This paper proposes a cell-level implementation of current-sensorless on-board impedance measurements in multi-cell battery stacks. In the proposed method, the current required for the impedance calculations is estimated based on the voltage measurements and the equivalent circuit resistance compensated by the circuit inductance. Comprehensive introduction on the appropriate battery stack prototype with on-board impedance measurements is presented. The performances of the methods and prototype are validated by experiments on several different different sets of nickel-manganese-cobalt-oxide (NMC) Lithium-ion cells.

Lithium-ion batteries are essential for modern energy storage systems due to their high energy density and operational efficiency. However, their electrochemical behavior is influenced by temperature and State of Health (SOH), making accurate diagnostics vital. This study investigates the impedance characteristics of prismatic 50 Ah Nickel Manganese Cobalt (NMC) cells using Electrochemical Impedance Spectroscopy (EIS) across varying temperatures (25°C, 35°C, and 45°C), SOH levels, and State of Charge (SOC). EIS measurements were performed using a Biologic HCP-1005 Potentiostat in the frequency range of 10 mHz to 10 kHz. The objective is to explore how thermal and aging conditions affect impedance signatures, particularly ohmic and charge transfer resistance, to support the development of improved battery management strategies and predictive models for SOH, SOC, and internal temperature (IT) estimation.

The internal temperature of electrochemical accumulators is a crucial parameter that significantly impacts their aging and safety. In particular, the phenomenon of thermal runaway must be detected early due to its rapid progression and potentially catastrophic consequences. However, measuring the temperature of each cell within a battery pack is costly and typically only provides access to the external temperature of the elements. Moreover, as cell size increases, their thermal capacity also rises, leading to a significant time lag between the internal temperature and the surface temperature. Electrochemical Impedance Spectroscopy is a precise method for assessing electrochemical parameters and phenomena, which are closely correlated with the internal temperature of batteries; therefore, temperature estimation can be achieved using impedance measurements. This article presents an innovative, low-cost approach using an embedded version of the impedance spectroscopy technique to estimate the internal temperature of high-capacity 175 Ah Li-ion cells, which exhibit very low impedances (less than 1 m$\Omega$ on average). Experimental results demonstrate that embedded impedancemetry enables internal temperature estimation of individual cells in a battery pack with an RMSE of 1.5 $^{\circ }$ C.

Temperature monitoring is essential for preventing severe thermal failures in the battery management system (BMS). Therefore, accurately modeling the thermal dynamics, particularly under complex operation conditions such as cyclic charge–discharge, is crucial for effective battery management. In this article, a residual-enhanced fuzzy state-space modeling is proposed for the battery thermal process to achieve real-time temperature monitoring. First, an updated nominal distributed parameter system (DPS) is constructed, consisting of two components: a nominal part identified offline via Takagi–Sugeno (T–S) fuzzy approximation, and an updated part derived from the temporal residual state estimation of the residual extended state observer (ESO). Then, an online temporal model is established by integrating the temporal part of the updated nominal DPS with the residual ESO. In addition, a fuzzy spatial mapping filter (SMF) is designed to provide update signals for the online model under a few sensors. The convergence of the proposed online model will be demonstrated in Hilbert space. Finally, the proposed modeling method is applied to the battery thermal process for real-time temperature monitoring successfully.

All-Solid-State Batteries (ASSBs) offer enhanced safety and higher energy density compared to conventional Lithium-Ion Batteries (LiBs), but their thermal management is challenging due to time-varying thermal properties. The thermal behavior of ASSBs is modeled by five Ordinary Differential Equations (ODEs) representing the temperatures of the case surface (near the cathode and anode), cathode, electrolyte, and anode. These temperatures are driven by heat from the battery, derived from an electrochemical model using two Partial Differential Equations (PDEs) for Li+ ions concentration. This study presents an adaptive observer that adjusts thermal conductivities in real-time, accurately estimating ASSB temperatures. Simulations demonstrate that the observer effectively tracks time-varying conductivities, with estimation errors converging to zero and improving thermal management accuracy.

In the present era of transportation electrification, an integrated framework is developed in this paper for real-time estimation of the voltage and temperature in lithium-ion batteries (LIBs) based on a Sliding Mode Observer (SMO) approach. The study is based on a first-order electrical equivalent circuit model (1-RC model), augmented with thermal dynamics. The battery’s open circuit voltage (OCV) is modeled as a polynomial function of the state-of-charge (SOC), while the transient behavior is captured through a parallel RC network. For voltage estimation, the SMO is applied to accurately estimate the internal RC voltage drop, enabling the reconstruction of terminal voltage under dynamic current load profiles. In parallel, a thermal model is implemented to account for heat generation and dissipation, with a secondary SMO applied to enhance temperature estimation accuracy. Experimental data from Hybrid Pulse Power Characterization (HPPC) tests are utilized for validation and the performance is assessed by comparing measured and estimated values. The results demonstrate strong agreement between simulated and measured data, with reduced error margins-voltage and temperature Root Mean Squared Percentage Errors (RMSPEs) of 0.23% and 0.13% — confirming the accuracy, stability, and adaptability of the proposed SMO-based framework for advanced battery monitoring and state estimation applications.

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Accurate thermal parameter identification is critical for lithium-ion battery safety under fast charging. This paper proposes an online estimation method based on an extended state parameter observer (ESPO), which embeds disturbance terms into a first-order thermal model to track variations in thermal resistance, capacitance, and ambient conditions in real time. A lightweight multilayer perceptron (MLP) predicts internal resistance, improving heat generation estimation. Lyapunov analysis ensures stability, while experiments on a battery charging platform validate accurate parameter tracking and effective temperature regulation. Compared with offline and recursive methods, the proposed approach achieves superior accuracy, adaptability, and computational efficiency, offering a practical solution for real-time thermal state estimation and safety management of lithium-ion batteries.

The internal states of lithium-ion batteries need to be carefully monitored during operation to manage energy and safety. In this article, we propose a thermal-enhanced adaptive interval observer for state-of-charge (SOC) and temperature estimation for a battery pack. For a large battery pack with hundreds or thousands of heterogeneous cells, each individual cell characteristic is different from others. Practically, applying estimation algorithms on each and every cell would be mathematically and computationally intractable since battery packs are often characterized by combinations of differential equations (state dynamics) and algebraic constraints (Kirchhoff’s laws). These issues are tackled using an interval observer based on monotone/cooperative system theory, whose novelty lies in considering cell heterogeneity and state-dependent parameters as unknown, but bounded uncertainties. The resulting interval observer maps the bounded uncertainties to a feasible set of SOC and temperature estimation for all cells in the pack at each time instant. This work also addresses the significant conservatism under extreme conditions with large currents via a thermal-enhanced adaptive scheme. The proposed interval estimation is scalable and computationally tractable since it is independent of the number of cells in a pack, as numerically demonstrated in a comparison with respect to a state-of-the-art single-cell state observer. The stability and inclusion of the adaptive interval observer are proven and validated through simulations.

Estimating the state of charge (SoC), state of health (SOH), and core temperature under internal faults will significantly improve the battery management system’s (BMS’s) autonomy and accuracy in range prediction. This article presents a neural network (NN)-based state estimation scheme that can estimate the SoC, core temperature, and SOH under internal faults in lithium-ion batteries (LIBs). First, we propose a model-based internal fault detection scheme by employing an SOH-coupled electro-thermal-aging (ETA) model of the LIB. Then, a nonlinear observer is used to estimate the proposed SOH-coupled model’s healthy states for the residual generation. The fault diagnosis scheme compares the output voltage and surface temperature residuals against the designed adaptive threshold to detect thermal faults. The adaptive threshold effectively alleviates the false positives due to degradation and model uncertainties of the battery under no-fault conditions. Upon fault detection, we employ an additional NN-based observer in the second step to learn the faulty dynamics. A novel NN weight tuning algorithm is proposed using the measured voltage, surface temperature, and estimated healthy states. The convergence of the nonlinear and NN-based observer state estimation errors is proven using the Lyapunov theory. Finally, numerical simulation results are presented.

During a decade of electric vehicle market rapid growth, Lithium-ion batteries have played a leading role thanks to their high power and energy density. Nonetheless, they still face many challenges, such as the influence of the State of Charge(SOC), ambient temperature and current rates on their life cycle. Which makes battery states prediction and thermal management essential to improve the Li-ion battery performance. Combining a three-state equivalent circuit model and a two-state thermal model, this paper proposes a coupled electro-thermal battery model capturing the battery state of charge, surface and core temperatures. Knowing these three key factors ensures better control of the battery operation conditions to prevent excessive heat generation. The model is expressed in a state-space form to allow battery state estimation, SOC and thermal prediction. A simple state observer and a robust nonlinear state estimator for SOC prediction are presented and compared. Then a nonlinear observer for core and surface temperature is modeled, and the obtained results are discussed.

Accurate monitoring of the internal statuses is highly valuable for the management of the lithium-ion battery (LIB). This article proposes a thermal-model-based method for multistate joint observation, enabled by a novel smart battery design with an embedded and distributed temperature sensor. In particular, a novel smart battery is designed by implanting the distributed fiber optical sensor internally and externally. This promises a real-time distributed measurement of LIB internal and surface temperature with a high space resolution. Following this endeavor, a low-order joint observer is proposed to coestimate the thermal parameters, heat generation rate, state of charge, and maximum capacity. Experimental results disclose that the smart battery has space-resolved self-monitoring capability with high reproducibility. With the new sensing data, the heat generation rate, state of charge, and maximum capacity of LIB can be observed precisely in real time. The proposed method validates to outperform the commonly-used electrical-model-based method regarding the accuracy and the robustness to battery aging.

No abstract available

No abstract available

Fast charging is crucial for applications of lithium-ion batteries in energy power systems. In this paper, a novel optimal charging strategy based on the model predictive control considering lithium plating and cell temperature is proposed. This method maximizes the charging speed while maintaining battery performance. It addresses constraints on the input current, the inner anode potential, and the temperature to prevent lithium plating and thermal safety issues. A thermal-coupled electrode equivalent circuit model is developed to observe the battery internal states with limited computation. A state observer based on the extended Kalman filter and a particle swarm optimizer is adopted in the MPC framework. The capability of this charging strategy is demonstrated via simulation and the result reveals that the battery can be charged to 86.6% of the full capacity in 17 minutes with accurate control of the anode potential and temperature. Compared with other charging protocols, the proposed method presents significant superiority. Besides, the optimal charging strategy is practical for onboard applications.

High-capacity energy storage systems rely on interconnected electrochemical cells to ensure stable power delivery and efficiency. During operation, energy transfer processes generate significant thermal output, which can impact system integrity. Managing this thermal effect is critical to maintaining optimal performance and preventing overheating. Excessive temperature rise can disrupt functionality, necessitating precise control of heat distribution and dissipation. This study investigates the dynamic thermal behavior of energy storage cells during periods of energy intake and release. It explores the mechanisms of heat generation, transfer, and loss to surrounding environments, aiming to predict thermal conditions under various operational states. The findings contribute to enhancing the design and operation of energy storage systems, ensuring longevity, reliability, and safety.

Despite the ever-increasing use across different sectors, the lithium-ion batteries (LiBs) have continually seen serious concerns over their thermal vulnerability. The LiB operation is associated with the heat generation and buildup effect, which manifests itself more strongly, in the form of highly uneven thermal distribution, for a LiB pack consisting of multiple cells. If not well monitored and managed, the heating may accelerate aging and cause unwanted side reactions. In extreme cases, it will even cause fires and explosions, as evidenced by a series of well-publicized incidents in recent years. To address this threat, this paper, for the first time, seeks to reconstruct the three-dimensional temperature field of a LiB pack in real time. The major challenge lies in how to acquire a high-fidelity reconstruction with constrained computation time. In this study, a three-dimensional thermal model is established first for a LiB pack configured in series. Although spatially resolved, this model captures spatial thermal behavior with a combination of high integrity and low complexity. Given the model, the standard Kalman filter is then distributed to attain temperature field estimation at substantially reduced computational complexity. The arithmetic operation analysis and numerical simulation illustrate that the proposed distributed estimation achieves a comparable accuracy as the centralized approach but with much less computation. This work can potentially contribute to the safer operation of the LiB packs in various systems dependent on LiB-based energy storage, potentially widening the access of this technology to a broader range of engineering areas.

The temperature distribution in the battery significantly impacts the short-term and long-term performance of battery systems. Therefore, efficient, safe, and reliable battery system operation requires an accurate estimation of the temperature field. The current industry standard for sensors to battery cell ratio is quite frugal. Thus, the problem of sensor placement for accurate temperature estimation becomes non-trivial, especially for large-scale systems. In this paper, we explore a greedy approach for sensor placement suitable for large-scale battery systems. An observer to estimate the thermal field is designed in an $\mathcal{H}_{\infty}$ framework while simultaneously minimizing the sensor precisions, thus lowering the overall thermal management system's economic cost.

In this article we investigate a model for the temperature within a Lithium-Ion battery. The model takes the form of a parabolic PDE for the temperature coupled with two elliptic PDE's for the electric potential within the solid and electrolyte phases. The primary difficulty comes from the coupling term, which is given by the Butler-Volmer equation. It features an exponential nonlinearity of both the electric potentials and the reciprocal of the temperature. Another difficulty arising in the temperature equation are the gradients of the electric potentials squared showing up on the right-hand side. Due to the nonlinearity, meaningful estimates for the temperature are currently not known. In spite of this, our investigation reveals the local existence of continuous temperature for the Lithium-Ion Battery.

Many filters have been proposed in recent decades for the nonlinear state estimation problem. The linearization-based extended Kalman filter (EKF) is widely applied to nonlinear industrial systems. As EKF is limited in accuracy and reliability, sequential Monte-Carlo methods or particle filters (PF) can obtain superior accuracy at the cost of a huge number of random samples. The unscented Kalman filter (UKF) can achieve adequate accuracy more efficiently by using deterministic samples, but its weights may be negative, which might cause instability problem. For Gaussian filters, the cubature Kalman filter (CKF) and Gauss Hermit filter (GHF) employ cubature and respectively Gauss-Hermite rules to approximate statistic information of random variables and exhibit impressive performances in practical problems. Inspired by this work, this paper presents a new nonlinear estimation scheme named after geometric unscented Kalman filter (GUF). The GUF chooses the filtering framework of CKF for updating data and develops a geometric unscented sampling (GUS) strategy for approximating random variables. The main feature of GUS is selecting uniformly distributed samples according to the probability and geometric location similar to UKF and CKF, and having positive weights like PF. Through such way, GUF can maintain adequate accuracy as GHF with reasonable efficiency and good stability. The GUF does not suffer from the exponential increase of sample size as for PF or failure to converge resulted from non-positive weights as for high order CKF and UKF.

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors.

The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational inference approaches, particularly under the more realistic non-mean-field (NMF) assumption, including extensive training effort, compromised inference accuracy, and infeasibility for online applications, among others. In this paper, we tackle these challenges by incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the NMF variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO). Moreover, owing to the streamlined parameterization via the EnKF, the new GPSSM model can be easily accommodated in online learning applications. We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting. We also provide detailed analysis and fresh insights for the proposed algorithms. Comprehensive evaluation across diverse real and synthetic datasets corroborates the superior learning and inference performance of our EnKF-aided variational inference algorithms compared to existing methods.

Accurate state estimation of large-scale lithium-ion battery packs is necessary for the advanced control of batteries, which could potentially increase their lifetime through e.g. reconfiguration. To tackle this problem, an enhanced reduced-order electrochemical model is used here. This model allows considering a wider operating range and thermal coupling between cells, the latter turning out to be significant. The resulting nonlinear model is exploited for state estimation through unscented Kalman filters (UKF). A sensor network composed of one sensor node per battery cell is deployed. Each sensor node is equipped with a local UKF, which uses available local measurements together with additional information coming from neighboring sensor nodes. Such state estimation scheme gives rise to a partition-based unscented Kalman filter (PUKF). The method is validated on data from a detailed simulator for a battery pack comprised of six cells, with reconfiguration capabilities. The results show that the distributed approach outperforms the centralized one in terms of computation time at the expense of a very low increase of mean-square estimation error.

Accurate and computationally light algorithms for estimating the State of Charge (SoC) of a battery's cells are crucial for effective battery management on embedded systems. In this letter, we propose an Adaptive Extended Kalman Filter (AEKF) for SoC estimation using a covariance adaptation technique based on maximum likelihood estimation - a novelty in this domain. Furthermore, we tune a key design parameter - the window size - to obtain an optimal memory-performance trade-off, and experimentally demonstrate our solution achieves superior estimation accuracy with respect to existing alternative methods. Finally, we present a fully custom implementation of the AEKF for a general-purpose low-cost STM32 microcontroller, showing it can be deployed with minimal computational requirements adequate for real-world usage.

Essential to various practical applications of lithium-ion batteries is the availability of accurate equivalent circuit models. This paper presents a new coupled electro-thermal model for batteries and studies how to extract it from data. We consider the problem of maximum likelihood parameter estimation, which, however, is nontrivial to solve as the model is nonlinear in both its dynamics and measurement. We propose to leverage the Bayesian optimization approach, owing to its machine learning-driven capability in handling complex optimization problems and searching for global optima. To enhance the parameter search efficiency, we dynamically narrow and refine the search space in Bayesian optimization. The proposed system identification approach can efficiently determine the parameters of the coupled electro-thermal model. It is amenable to practical implementation, with few requirements on the experiment, data types, and optimization setups, and well applicable to many other battery models.

We proposed a new estimation algorithm of extended Kalman filter (EKF) based on improved Thevenin model; Experiments were carried out to verify the validity with seven 4Ah lithium cobalt acid batteries in series. The experimental results showed that when using the algorithm, the estimation error of SOC is in the scope of error allowed, and the requirement of online SOC estimation can be satisfied.

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. We show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an "ensemble of Kalman filters" operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, we consider the construction of the PKF through an "ensemble" of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). We show that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, we also introduce a re-sampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.

Equivalent Circuit Model(ECM)has been widelyused in battery modeling and state estimation because of itssimplicity, stability and interpretability.However, ECM maygenerate large estimation errors in extreme working conditionssuch as freezing environmenttemperature andcomplexcharging/discharging behaviors,in whichscenariostheelectrochemical characteristics of the battery become extremelycomplex and nonlinear.In this paper,we propose a hybridbattery model by embeddingneural networks as 'virtualelectronic components' into the classical ECM to enhance themodel nonlinear-fitting ability and adaptability. First, thestructure of the proposed hybrid model is introduced, where theembedded neural networks are targeted to fit the residuals of theclassical ECM,Second, an iterative offline training strategy isdesigned to train the hybrid model by merging the battery statespace equation into the neural network loss function. Last, thebattery online state of charge (SOC)estimation is achieved basedon the proposed hybrid model to demonstrate its applicationvalue,Simulation results based on a real-world battery datasetshow that the proposed hybrid model can achieve 29%-64%error reduction for $OC estimation under different operatingconditions at varying environment temperatures.

The impedance of a Li-ion battery contains information about its state of charge (SOC), state of health (SOH) and remaining useful life (RUL). Commonly, electrochemical impedance spectroscopy (EIS) is used as a nonparametric data-driven technique for estimating this impedance from current and voltage measurements. In this article, however, we propose a consistent parametric estimation method based on a fractional order equivalent circuit model (ECM) of the battery impedance. Contrary to the nonparametric impedance estimate, which is only defined at the discrete set of excited frequencies, the parametric estimate can be evaluated in every frequency of the frequency band of interest. Moreover, we are not limited to a single sine or multisine excitation signal. Instead, any persistently exciting signal, like for example a noise excitation signal, will suffice. The parametric estimation method is first validated on simulations and then applied to measurements of commercial Samsung 48X cells. For now, only batteries in rest, i.e. at a constant SOC after relaxation, are considered.

Operando impedance measurements are promising for monitoring batteries in the field. In this work, we present pseudo-random sequences for low-cost operando battery impedance measurements. The quadratic-residue ternary sequence and direct-synthesis ternary sequence exhibit specific properties related to eigenvectors of the discrete Fourier transform matrix that allow computationally efficient compensation for drifts and transients in operando impedance measurements. We describe the application of pseudo-random sequences and provide the data processing required to suppress drift and transients, validated on simulations. Finally, we perform experimental operando impedance measurements on a Li-ion battery cell during fast-charging, demonstrating the applicability of the proposed method. It's low-cost hardware requirements, fast measurements, and simple data-processing make the method practical for embedding in battery management systems.

The short diffusion lengths in insertion battery nanoparticles render the capacitive behavior of bounded diffusion, which is rarely observable with conventional larger particles, now accessible to impedance measurements. Coupled with improved geometrical characterization, this presents an opportunity to measure solid diffusion more accurately than the traditional approach of fitting Warburg circuit elements, by properly taking into account the particle geometry and size distribution. We revisit bounded diffusion impedance models and incorporate them into an overall impedance model for different electrode configurations. The theoretical models are then applied to experimental data of a silicon nanowire electrode to show the effects of including the actual nanowire geometry and radius distribution in interpreting the impedance data. From these results, we show that it is essential to account for the particle shape and size distribution to correctly interpret impedance data for battery electrodes. Conversely, it is also possible to solve the inverse problem and use the theoretical "impedance image" to infer the nanoparticle shape and/or size distribution, in some cases, more accurately than by direct image analysis. This capability could be useful, for example, in detecting battery degradation in situ by simple electrical measurements, without the need for any imaging.

Non-invasive parametrisation of physics-based battery models can be performed by fitting the model to electrochemical impedance spectroscopy (EIS) data containing features related to the different physical processes. However, this requires an impedance model to be derived, which may be complex to obtain analytically. We have developed the open-source software PyBaMM-EIS that provides a fast method to compute the impedance of any PyBaMM model at any operating point using automatic differentiation. Using PyBaMM-EIS, we investigate the impedance of the single particle model, single particle model with electrolyte (SPMe), and Doyle-Fuller-Newman model, and identify the SPMe as a parsimonious option that shows the typical features of measured lithium-ion cell impedance data. We provide a grouped parameter SPMe and analyse the features in the impedance related to each parameter. Using the open-source software PyBOP, we estimate 18 grouped parameters both from simulated impedance data and from measured impedance data from a LG M50LT lithium-ion battery. The parameters that directly affect the response of the SPMe can be accurately determined and assigned to the correct electrode. Crucially, parameter fitting must be done simultaneously to data across a wide range of states-of-charge. Overall, this work presents a practical way to find the parameters of physics-based models.

Electrochemical impedance spectra for battery electrodes are usually interpreted using models that assume isotropic active particles, having uniform current density and symmetric diffusivities. While this can be reasonable for amorphous or polycrystalline materials with randomly oriented grains, modern electrode materials increasingly consist of highly anisotropic, single-crystalline, nanoparticles, with different impedance characteristics. In this paper, analytical expressions are derived for the impedance of anisotropic particles with tensorial diffusivities and orientation-dependent surface reaction rates and capacitances. The resulting impedance spectrum contains clear signatures of the anisotropic material properties and aspect ratio, as well as statistical variations in any of these parameters.

In this work we analyse the local nonlinear electrochemical impedance spectroscopy (NLEIS) response of a lithium-ion battery and estimate model parameters from measured NLEIS data. The analysis assumes a single-particle model including nonlinear diffusion of lithium within the electrode particles and asymmetric charge transfer kinetics at their surface. Based on this model and assuming a moderately-small excitation amplitude, we systematically derive analytical formulae for the impedances up to the second harmonic response, allowing the meaningful interpretation of each contribution in terms of physical processes and nonlinearities in the model. The implications of this for parameterization are explored, including structural identifiability analysis and parameter estimation using maximum likelihood, with both synthetic and experimentally measured impedance data. Accurate fits to impedance data are possible, however inconsistencies in the fitted diffusion timescales suggest that a nonlinear diffusion model may not be appropriate for the cells considered. Model validation is also demonstrated by predicting time-domain voltage response using the parameterized model and this is shown to have excellent agreement with measured voltage time-series data (11.1 mV RMSE).

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver's ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

Optimal cooling that minimises thermal gradients and the average temperature is essential for enhanced battery safety and health. This work presents a new modelling approach for battery cells of different shapes by integrating Chebyshev spectral-Galerkin method and model component decomposition. As a result, a library of reduced-order computationally efficient battery thermal models is obtained, characterised by different numbers of states. These models are validated against a high-fidelity finite element model and are compared with a thermal equivalent circuit (TEC) model under real-world vehicle driving and battery cooling scenarios. Illustrative results demonstrate that the proposed model with four states can faithfully capture the two-dimensional thermal dynamics, while the model with only one state significantly outperforms the widely-used two-state TEC model in both accuracy and computational efficiency, reducing computation time by 28.7%. Furthermore, our developed models allow for independent control of tab and surface cooling channels, enabling effective thermal performance optimisation. Additionally, the proposed model's versatility and effectiveness are demonstrated through various applications, including the evaluation of different cooling scenarios, closed-loop temperature control, and cell design optimisation.