Battery Capacity Estimation Research Articles

Battery Capacity Estimation Based on Incremental Capacity Analysis Considering Charging Current Rate

Incremental capacity analysis (ICA) is widely used in the battery decay mechanism analysis since the features of battery incremental capacity (IC) curves are closely related to battery aging and maximum available capacity. However, the traditional ICA method to estimate battery capacity mainly focuses on a single charging condition, and the influence of charging current on IC curves is ignored. In this paper, an adaptive capacity estimation method based on ICA considering the charging current is established. First, the charging experiments using different charging current rates under different battery aging statuses are designed and conducted. Then, the relationship between battery maximum available capacity, IC curve features, and charging current is investigated. Furthermore, the fitting method and data-driven method considering charging current are proposed and compared. Finally, the capacity estimation results prove the accuracy and adaptability of the proposed method.

Lithium-ion battery capacity estimation based on open circuit voltage identification using the iteratively reweighted least squares at different aging levels

In traditional incremental SOC (stage of charge)-capacity method, errors of the selected SOC points inevitably lead to inaccurate capacity estimation. In this paper, a capacity estimation method based on OCV (open circuit voltage) identification and IRLS (iteratively reweighted least squares) algorithm method is proposed. Firstly, the accuracy and complexity of three parameter identification schemes of first-order RC model at different aging levels are studied with the forgetting factor recursive least squares algorithm. Through the online identified OCV by the optimal scheme, the full interval SOC estimation can be obtained indirectly. Finally, the capacity is estimated using the full interval SOC estimation with IRLS algorithm, which avoids the randomness of the SOC point selection, and solves the problem of possible outliers in the SOC estimation or the unknown variance of the random error of the SOC gain. Through the designed aging experiment, the capacity estimation accuracy is verified under different life conditions. The results show that the estimation accuracy of this method is high and the error does not exceed 2.5%.

A data-fusion framework for lithium battery health condition Estimation Based on differential thermal voltammetry

Battery state foretasting and health management are significant tasks for ensuring safety and stability of battery systems. Accurate state estimation can not only provide valuable parameters for energy management but also may prolong battery usage lifespan. Comprehensive theoretical analysis and practical application, differential thermal voltammetry analysis method has great potentials in actual operation. This paper proposes a closed-loop battery capacity estimation framework, Gaussian process regression and multi-output Gaussian process regression for constructing battery dynamic state-space function, to improve the accuracy and robustness of battery SOH estimation. Firstly, a time-series model of battery capacity degradation is established as the state equation using Gaussian process regression. Secondly, two strong correlation indicators are treated as observed parameters to construct an observation equation through multi-output Gaussian process regression, where the health indicators are extracted from the partial smoothed curves by two filter methods. Thirdly, particle filter algorithm is employed to correct the prior estimated capacity and suppress noise perturbations for achieving closed-loop control. Additionally, the performances of particle filter algorithm with different particle sizes are discussed and analyzed from accuracy and computational time aspects. Verification of three types of batteries indicates that the proposed method has an excellent capability for battery capacity estimation.

A method for capacity prediction of lithium-ion batteries under small sample conditions

Accurate life prediction of lithium-ion battery is very important for the safe operation of battery system. At present, the data-driven life prediction method is an effective method. However, it is difficult to obtain full life cycle data of long-life lithium batteries, which leads to low accuracy of prediction results. In addition, the degradation of lithium-ion batteries has different trends in different stages, the commonly used methods are insufficient to describe global time variables which make it difficult to adapt to changes in different stages of lithium-ion battery capacity degradation. To solve the above problems, the paper proposes a deep adaptive continuous time-varying cascade network based on extreme learning machines (CTC-ELM) under the condition of small samples. First, a virtual sample generation method based on multi-population differential evolution is proposed, which uses multi-distribution overall trend diffusion technology to adaptively determine the virtual sample range, and combines with the improved differential evolution algorithm to achieve small sample data amplification. Then, a new prediction network with CTC-ELM is constructed. Finally, it is verified on different data sets. Experiments show that the method proposed can effectively expand the sample set of lithium-ion batteries and achieve high accuracy in the estimation of lithium-ion battery capacity.

Capacity estimation of batteries: Influence of training dataset size and diversity on data driven prognostic models

Prognostics of batteries involve state estimation and remaining useful life (RUL) prediction. Various data-driven approaches are being studied to achieve accurate RUL predictions and SOH estimations to ensure safety and reliability of battery systems. The Gaussian Process Regression (GPR) is a statistical approach that accommodates the nonlinear nature and small sample size data to effectively predict the RUL of lithium-ion batteries. Artificial Neural Networks (ANN) have the ability to approximate nonlinear data and since battery degradation is a nonlinear process, neural networks-based models can provide accurate RUL predictions for lithium-ion batteries. In this paper, both the GPR model and ANN model approaches are implemented on the NASA PCoE battery datasets and the predictions are compared. The model training and validation is performed by splitting the data into various proportions (30:70%, 50:50%, and 70:30% for training: validation). Furthermore, the model's prediction accuracy is compared with respect to single vs multi-variable data and single battery data vs combined multiple battery data. The approach improves the prediction accuracy with the models exhibiting low RMSE values of 0.0181 and 0.0367 for GPR and ANN models, respectively, for B0018 and RMSE values of 0.1516 and 0.0810 for GPR and ANN models, respectively, for B0048.

A remaining capacity estimation approach of lithium-ion batteries based on partial charging curve and health feature fusion

Health condition monitoring of lithium-ion batteries plays a crucial role in guaranteeing the reliability and safety of energy storage system. However, it is difficult to directly measure state of health of cell, which is sensitive to the complex application scenarios and related to battery internal physicochemical characters. This paper proposes a remaining capacity prediction technique for lithium-ion batteries based on partial charging curve and health feature fusion. Here, health features are extracted from partial charging profile and the fused health feature is obtained via canonical correlation analysis, which is utilized to improve feature correlation and reduce data dimension. A battery aging model is established by Gaussian process regression and validation is conducted on six battery data sets from National Aeronautics and Space Administration (NASA) and University of Oxford. The results show that the proposed method can achieve reliable and accurate battery capacity estimation.

A health indicator extraction and optimization for capacity estimation of Li-ion battery using incremental capacity curves

Accurate lithium battery online capacity and remaining useful life (RUL) estimation are critical to increasing penetration of electric vehicles. Motivated by this, health indicators (HIs) extraction and optimization using incremental capacity curves are proposed. This paper reports a straightforward approach to smooth the noise on IC curves, thereby capturing accurate and reliable HIs. To prevent overfitting in machine learning, a combined weighting method is emphasized to reduce the dimensionality of HIs. It is then used in the modeling of battery capacity estimation as the improved Gaussian process regression is applied. In this framework, results show that the correlation between the battery capacity and dimension-reducing HIs is desirable. Analysis results reveal the above measures' trustworthiness, with the average error of the six batteries is 2.3% under the cross-validation test. What's more, a set of different types of batteries are used to verify the robustness of this method.

Screening of Retired Lithium-Ion Batteries Using Incremental Capacity Charging Curve-Based Residual Capacity Estimation Method for Facilitating Sustainable Circular Lithium-Ion Battery System

Abstract The rapidly growing deployment of lithium-ion batteries in electric vehicles is associated with a great waste of natural resource and environmental pollution caused by manufacturing and disposal. Repurposing the retired lithium-ion batteries can extend their useful life, creating environmental and economic benefits. However, the residual capacity of retired lithium-ion batteries is unknown and can be drastically different owing to various working history and calendar life. In this study, we used the incremental capacity (IC) curve to estimate the residual capacity of waste power batteries. First, through experimental means, the parameters of the battery and the IC charging curve are measured. Second, to achieve rapid capacity estimation, a battery capacity estimation method based on the adaptive genetic algorithm-back propagation neural network (AGA-BPNN) is proposed and compared with other classic machine learning methods. The proposed algorithm reduced the error of capacity estimation to 3%. Finally, through the analysis of the IC curve, a method for identifying aging mechanism of large-scale decommissioned batteries is obtained. This research provides effective support for the capacity-based classification of large-scale decommissioned power batteries.

Capacity estimation of lithium-ion batteries based on Gaussian process regression and feature selection

Capacity estimation of lithium-ion batteries based on Gaussian process regression and feature selection

A data-driven approach for capacity estimation of batteries based on voltage dependent health indicators

Battery capacity estimation plays an important role in the normal operation of electric vehicles. In this work, we presented a data-driven approach for capacity estimation of batteries based on voltage dependent health indicators. A difference-based model of discharge voltage and capacity was built. Next, two health indicators are constructed from partial voltage curves, and correlations between capacity and health indicators are investigated. Afterward, the capacity estimation approach based on Gaussian process regression model is expounded. To validate the accuracy of the proposed method, a case study is carried out. Results demonstrate that RMSE and RMSPE of capacity estimation are lower than 1% compared with actual capacity.

A novel combined multi-battery dataset based approach for enhanced prediction accuracy of data driven prognostic models in capacity estimation of lithium ion batteries

To ensure smooth and reliable operations of battery systems, reliable prognosis with accurate prediction of State of Health of lithium ion batteries is of utmost importance. However, battery degradation is a complex challenge involving many electrochemical reactions at anode, separator, cathode and electrolyte/electrode interfaces. Also, there is significant effect of the operating conditions on the battery degradation. Various machine learning techniques have been applied to estimate the capacity and State of Health of lithium ion batteries to ensure reliable operation and timely maintenance. In this paper, we study the Gaussian Process Regression (GPR) and Support Vector Machine (SVM) model-based approaches in estimating the capacity and State of Health of batteries. Battery capacity and State of Health estimations are carried out using GPR and SVM models and the predictions comparatively studied for accuracy based on RMSE values. The prediction accuracy is further compared with respect to single sensor and multi sensor data. Further, a combined multi battery data set model is used to improve the prediction accuracy. Combining the data of multiple batteries with similar operating conditions for training a model resulted in higher prediction accuracy.

A method for capacity estimation of lithium-ion batteries based on adaptive time-shifting broad learning system

Accurate capacity estimation of lithium-ion batteries can improve the safety and reliability of equipment. Deep learning provides a new approach for capacity estimation. However, it is still difficult to adapt to the changes in different stages of capacity degradation due to many and complex parameters in deep structure network and the time-invariant model parameters. Considering that Broad Learning System is a neural network independent of deep structure, which has a simple single hidden layer structure and fewer parameters, this paper proposes an Adaptive Time-shifting Broad Learning System (ATBLS) capacity estimation model. For input layer, the input data of each time step is combined with the output of previous time step to get a new input, so as to provide local information to hidden unit of the network and provide guidance for local parameters. For hidden layer, the hidden unit of each time step is weighted-fused with the hidden unit of previous time step to update the parameters, so as to reflect the long-term dynamics of sequence. The experiment are conducted on three different data sets. And the effectiveness of ATBLS is verified by comparing with other methods.

Sequent extended Kalman filter capacity estimation method for lithium-ion batteries based on discrete battery aging model and support vector machine

Precise battery capacity estimation plays an important role in the future intelligent battery management system. In this paper, a fusion estimation method based on support vector machine and discrete battery aging model is put forward to enhance the online capacity estimation accuracy of lithium-ion batteries under variable temperature conditions. During the constant current charging process, the support vector machine is developed to estimate the battery capacity, which first trains a single 18650 battery offline and then tests the accuracy of the model using two other batteries of the same type intermittently. Subsequently, the discrete aging model of the battery is proposed to continuously estimate the capacity of the battery. However, unmodelled dynamics between battery aging model and real physical battery is easily occur in the process of modeling, which affects the accuracy and robustness of the model. Therefore, a sequent extended Kalman filter algorithm is deployed for solving the problem. The first Kalman filter takes the identified value of support vector machine as observation value to update the model parameters of discrete battery aging model. The second Kalman filter fuses the identified value of support vector machine and the discrete battery aging model after updating model parameters to improve the precision of online battery capacity estimation. The experimental results indicate that the proposed discrete battery aging model and support vector machine have good applicability, and the algorithm used can online modify the parameters of the model. When the model parameters are modified four times, the fusion estimation error is less than 2%.

Lithium-ion battery capacity estimation — A pruned convolutional neural network approach assisted with transfer learning

Online battery capacity estimation is a critical task for battery management system to maintain the battery performance and cycling life in electric vehicles and grid energy storage applications. Convolutional Neural Networks, which have shown great potentials in battery capacity estimation, have thousands of parameters to be optimized and demand a substantial number of battery aging data for training. However, these parameters require massive memory storage while collecting a large volume of aging data is time-consuming and costly in real-world applications. To tackle these challenges, this paper proposes a novel framework incorporating the concepts of transfer learning and network pruning to build compact Convolutional Neural Network models on a relatively small dataset with improved estimation performance. First, through the transfer learning technique, the Convolutional Neural Network model pre-trained on a large battery dataset is transferred to a small dataset of the targeted battery to improve the estimation accuracy. Then a contribution-based neuron selection method is proposed to prune the transferred model using a fast recursive algorithm, which reduces the size and computational complexity of the model while maintaining its performance. The proposed model is capable of achieving fast online capacity estimation at any time, and its effectiveness is verified on a target dataset collected from four Lithium iron phosphate battery cells, and the performance is compared with other Convolutional Neural Network models. The test results confirm that the proposed model outperforms other models in terms of accuracy and computational efficiency, achieving up to 68.34% model size reduction and 80.97% computation savings.

Batteries State of Health Estimation via Efficient Neural Networks With Multiple Channel Charging Profiles

The prognostics and health management (PHM) plays the main role to handle the risk of failure before its occurrence. Next, it has a broad spectrum of applications including utility networks, energy storage systems (ESS), etc. However, an accurate capacity estimation of batteries in ESS is mandatory for their safe operations and decision making policy. ESS comprises of different storage mechanisms such as batteries, capacitors, etc. Consequently, the measurement of different charging profiles (CPs) has a strong relation to battery capacity. These profiles include temperature (T), voltage (V), and current (I) where the CPs patterns vary as the battery ages with cycles. Consequently, estimating a battery capacity, the conventional methods practice single channel charging profile (SCCP) and hop multiple channel CPs (MCCPs) that cause incorrect battery health estimation. To tackle these issues, this article proposes MCCPs based battery management system (BMS) to estimate batteries health/capacity through the deep learning (DL) concept where the patterns in these CPs are changed as the battery ages with time and cycles. Thus, we deeply investigate both machine learning (ML) and DL based methods to provide a concrete comparative analysis of our method. The adaptive boosting (AB) and support vector regression (SVR) are widely compared with long short-term memory (LSTM), multi-layer perceptron (MLP), bi-directional LSTM (BiLSTM), and convolutional neural network (CNN) to attain the appropriate approach for battery capacity and state of health (SOH) estimation. These approaches have a high learning capability of inter-relation between the battery capacity and variation in CPs patterns. To validate and verify the proposed technique, we use NASA battery dataset and experimentally prove that BiLSTM outperforms all the approaches and obtains the smallest error values for MAE, MSE, RMSE, and MAPE using MCCPs compared to SCCP.

Data Driven Estimation of Electric Vehicle Battery State of Charge Informed By Multi-Physics Modeling

State of charge (SOC) estimation in lithium-ion batteries (LIBs) is a crucial task of the battery management system (BMS) in electric vehicle (EV) applications. An accurate evaluation of the remaining capacity in a battery is cumbersome due to the non-linear and coupled behavior of the physical processes involved in the battery operation, in particular when LIBs is integrated in dynamic systems with many components such as in EV. With the continued progress in the development of data driven models, different machine learning (ML) and, more specifically, deep learning (DL) techniques have been proposed to predict the SOC in EV.1–4 While these models have been proven to be effective in estimating the SOC variation, the reliability of learning-based algorithms is highly dependent on the data collected for the training and validation purposes. The most straightforward methodology for data collection consists of discharging a lithium-ion cell in a laboratory by applying a discharge current which aims to represent the vehicle’s operation. However, such an approach could not allow to generate data representing realistic driving conditions since the dynamics of components, such as the electric motor and the powertrain system, which have an impact on the SOC and external conditions such as the speed of the wind are not taken into account. In this work, we propose a modeling framework based upon Matlab/Simulink automotive simulations of EV in order to generate a dataset reflecting practical driving conditions. The generated datasets have been used to train ML and DL models for the final SOC estimation. In particular, the most accurate estimation of SOC is obtained with the Long Short Term Memory (LSTM) network, a Recurrent Neural Network (RNN) designed for times series predictions with long term dependencies. Furthermore, employing a multi-physics modeling of the LIBs’ operation comprising the electric motor, the powertrain system and the overall vehicle dynamic, allows to investigate the effect of EV’s driving on the electrochemical processes and reactions occurring inside the battery of different chemistries. For this purpose, we use an electrochemical model of LIBs developed in Comsol Multiphysics combined with EV simulation, in order to study the degradation of the battery as a result of multiple charge and discharge cycles representing the vehicle operation. In particular, formation/decomposition of the solid electrolyte interphase (SEI) at the negative electrode has been considered as a possible degradation phenomenon. Thus, in addition to the development of training data for learning based techniques for SOC estimation informed by EV simulations, the proposed modeling approach allows the investigation of the battery functionality and degradation under realistic driving conditions.(1) Álvarez Antón, J. C.; García Nieto, P. J.; de Cos Juez, F. J.; Sánchez Lasheras, F.; González Vega, M.; Roqueñí Gutiérrez, M. N. Battery State-of-Charge Estimator Using the SVM Technique. Appl. Math. Model. 2013, 37 (9), 6244–6253. https://doi.org/10.1016/j.apm.2013.01.024.(2) Hu, C.; Jain, G.; Schmidt, C.; Strief, C.; Sullivan, M. Online Estimation of Lithium-Ion Battery Capacity Using Sparse Bayesian Learning. J. Power Sources 2015, 289, 105–113. https://doi.org/10.1016/j.jpowsour.2015.04.166.(3) Kang, L. W.; Zhao, X.; Ma, J. A New Neural Network Model for the State-of-Charge Estimation in the Battery Degradation Process. Appl. Energy 2014, 121, 20–27. https://doi.org/10.1016/j.apenergy.2014.01.066.(4) Chemali, E.; Kollmeyer, P. J.; Preindl, M.; Ahmed, R.; Emadi, A. Long Short-Term Memory Networks for Accurate State-of-Charge Estimation of Li-Ion Batteries. IEEE Trans. Ind. Electron. 2018, 65 (8), 6730–6739. https://doi.org/10.1109/TIE.2017.2787586.

Data-Driven State of Health Prognostic Model Using a Global Vehicle Data-Set

Data-driven prediction for battery state estimation provides a simple alternative to standard electrical and/or electrochemical models. Recent efforts have used cycling data from laboratory measurements to predict the state of health (SOH) of a cell over its lifetime [1-5]. Laboratory measurements attempt to capture the expected conditions during aging, however, due to the complex situations experienced by electric vehicles during aging, it is not possible to represent each aging path in a laboratory experiment. Additionally, due to resource and time limitations, measurements extending beyond one year are rare. In this work, a global data-set of over 15,000 readings from 300 vehicles driven under real-world conditions is used to provide context on vehicle aging and as a training set for a data-driven SOH prediction model. This data differs significantly from traditional laboratory data in that it does not contain the time-series sampling of, for example, current and voltage over time, as used in most models- rather averaged data over several days, and sometimes months. At relatively frequent intervals during the life of the vehicle, variables such as state of charge, temperature, kilometers driven and others, are compiled as an average over the measurement interval, resulting in one value per measurement period. These averaged readings offer a snapshot into the conditions the vehicle experienced during the measurement period, but do not offer the same detail as what would be recorded in laboratory settings. From this data, a novel data-driven SOH prediction model is developed. The SOH prediction is compared against the onboard SOH estimation performed in the vehicle, which itself has been validated by the vehicle manufacturers. With a large number of samples, a data-driven approach to predicting the capacity of a vehicle is applied. Using Keras, a neural network API written for Python, a two-layer neural network was cross-validated with 50 % training data and 50 % testing data, achieving a high prediction accuracy using six input parameters. This method has the advantage over traditional SOH prediction models, such as semi-empirical and equivalent circuit models, in that it is able to predict the SOH of vehicles in dynamic aging conditions over many years and does not require time-series values of voltage and current as inputs, or cell parameterization, which are often inaccurate and incur high costs to measure. Barré, F. Saurd, M. Gérard, M. Montaru, D. Riu, Statistical Analysis for understanding and prediction battery degradations in real-life electric vehicle use. Journal of Power Sources 245 (2014) 846-856.Zou, X. Hu, H. Ma, S. Li, Combined State of Charge and State of Health estimation over lithium-ion battery cell cycle lifespan for electrical vehicles. Journal of Power Sources 273 (2015) 793-803You, S. Park, D. Oh, Real-time state-of-health estimation for electric vehicle batteries: A data-driven approach. Applied Energy 176 (2016) 92-103.Li, C. Zou, M. Berecibar, E. Nanini-Maury, J. C.-W. Chan, P. van den Bossche, J. Van Mierlo, N. Omar, Random forest regression for online capacity estimation of lithium-ion batteries. Applied Energy 232 (2018) 197-210.Richardson, M. A. Osborne, D. A. Howey, Gaussian process regression for forecasting battery state of health. Journal of Power Sources 357 (2017) 208-219. Figure 1

A partial charging curve-based data-fusion-model method for capacity estimation of Li-Ion battery

Accurate capacity estimation is crucial and challenging for guaranteeing safety and durability of Li-ion batteries. This work proposes a data-fusion-model method to estimate battery capacity using the partial charging curve. First, during the charging process, two representative battery ageing features are extracted from the partial incremental capacity curve smoothed by Locally Weighted Scatterplot Smoothing (LOWESS). Second, the dual Gaussian process regressions (GPRs) are employed to establish a data-driven battery ageing state-space representation, which takes battery capacity as the state variable and takes two ageing features as the input variables. Third, combining with the GPR-based battery state-space representation, Particle Filter (PF) is introduced to suppress the measurement noises and a Gaussian Process Particle Filter (GPPF) is built to estimate battery capacity. Meanwhile, the output capacity is fed back to the GPPF to update the battery ageing state-space representation. Finally, ageing experiments are conducted to validate the effectiveness of the proposed method. Meanwhile, GPR is implemented with the cycle and two ageing features for capacity estimation as a contrast. The results show that the proposed GPPF method can provide more accurate and robustness battery estimation results than GPR.

Fast battery capacity estimation using convolutional neural networks

Lithium-ion batteries have been widely used in electric vehicles, smart grids and many other applications as energy storage devices, for which the aging assessment is crucial to guarantee their safe and reliable operation. The battery capacity is a popular indicator for assessing the battery aging, however, its accurate estimation is challenging due to a range of time-varying situation-dependent internal and external factors. Traditional simplified models and machine learning tools are difficult to capture these characteristics. As a class of deep neural networks, the convolutional neural network (CNN) is powerful to capture hidden information from a huge amount of input data, making it an ideal tool for battery capacity estimation. This paper proposes a CNN-based battery capacity estimation method, which can accurately estimate the battery capacity using limited available measurements, without resorting to other offline information. Further, the proposed method only requires partial charging segment of voltage, current and temperature curves, making it possible to achieve fast online health monitoring. The partial charging curves have a fixed length of 225 consecutive points and a flexible starting point, thereby short-term charging data of the battery charged from any initial state-of-charge can be used to produce accurate capacity estimation. To employ CNN for capacity estimation using partial charging curves is however not trivial, this paper presents a comprehensive approach covering time series-to-image transformation, data segmentation, and CNN configuration. The CNN-based method is applied to two battery degradation datasets and achieves root mean square errors (RMSEs) of less than 0.0279 Ah (2.54%) and 0.0217 Ah (2.93% ), respectively, outperforming existing machine learning methods.

Online capacity estimation of lithium-ion batteries with deep long short-term memory networks

There is an increasing demand for modern diagnostic systems for batteries under real-world operation, specifically for the estimation of their state of health, for example, via their remaining capacity. The online estimation of the capacity of a cell is challenging due to the dynamic nature of cell aging and the limited variety of inputs available from a cell under operation. The scope of this work is the development of a data-driven capacity estimation model for cells under real-world working conditions with recurrent neural networks having long short-term memory capability. Voltage-time sensor data from the partial constant current phase charging curve is used as input, reflecting input availability in the real world. The network achieves a best-case mean absolute percentage error of 0.76% and is extremely robust while handling input noise. It also has the ability to handle variations in the length of the input time series and can generate a viable estimation even with an incomplete collection of input due to sensor errors. The model validation with several scenarios is done in a local embedded device, highlighting the use case of such models in future battery management systems.