Online State Of Charge Estimation Research Articles

Online Adaptive Model Identification and State of Charge Estimation for Vehicle-Level Battery Packs

Accurate state of charge (SOC) estimation of traction batteries plays a crucial role in energy and safety management for electric vehicles. Existing studies focus primarily on cell battery SOC estimation. However, numerical instability and divergence problems might occur for a large-size lithium-ion battery pack consisting of many cells. This paper proposes a high-performance online model identification and SOC estimation method based on an adaptive square root unscented Kalman filter (ASRUKF) and an improved forgetting factor recursive least squares (IFFRLS) for vehicle-level traction battery packs. The model parameters are identified online through the IFFRLS, where the conventional method might encounter numerical stability problems. By updating the square root of the covariance matrix, the divergence problem in the traditional unscented Kalman filter is solved in the ASRUKF algorithm, where the positive semi-definiteness of the covariance matrix is guaranteed. Combined with the adaptive noise covariance matched filtering algorithm and real-time compensation of system error, the proposed method solves the problem of ever-degrading estimation accuracy in the presence of time-varying noise with unknown statistical characteristics. Using a 66.2-kWh vehicle battery pack, we experimentally verified that the proposed algorithm could achieve high estimation accuracy with guaranteed numerical stability. The maximum error of SOC estimation can be bounded by 1%, and the root-mean-square error is as low as 0.47% under real-world vehicle operating conditions.

A Novel Transfer Learning-Based Cell SOC Online Estimation Method for a Battery Pack in Complex Application Conditions

The crucial function of a battery management system is to estimate the state of charge (SOC). However, complex application conditions like different temperatures, aging, and inconsistency between cells would cause a distribution difference between data domains and lead to a significant estimation error in the established SOC model. Transfer learning's domain adaptation offers a way to lessen the disparity in distribution across the data domains, and yet it also requires that the target space be the same across domains, which is challenging to do with the SOC online estimate. This article proposes a SOC differential processing method as well as designs a combined transfer learning method. As experiments of actual battery pack provided by China First Automobile Work-based confirmed, the proposed method can obtain precise and robust SOC estimation results with a mean absolute percentage error of less than 1.5%.

An improved adaptive weights correction-particle swarm optimization-unscented particle filter method for high-precision online state of charge estimation of lithium-ion batteries

An improved adaptive weights correction-particle swarm optimization-unscented particle filter method for high-precision online state of charge estimation of lithium-ion batteries

Battery SOC estimation from EIS data based on machine learning and equivalent circuit model

Estimating the state of charge (SOC) of batteries is fundamental for the proper management and safe operation of numerous systems, including electric vehicles, smart energy grids, and portable electronics. While there is no practical method for direct measurement of SOC, several estimation approaches have been developed, including a growing number of machine-learning-based techniques. Machine learning methods are intrinsically data-driven but can also benefit from a-priori knowledge embedded in a model. In this work, we first demonstrate, through exploratory data analysis, that it is possible to discriminate between different SOC from electrochemical impedance spectroscopy (EIS) measurements. Then we propose a SOC estimation approach based on EIS and an equivalent circuit model to provide a compact way to describe the frequency domain and time-domain behavior of the impedance of a battery. We experimentally validated this approach by applying it to a dataset consisting of EIS measurements performed on four lithium-ion cylindrical cells at different SOC values. The proposed approach allows for very efficient model training and produces a low-dimensional SOC classification model that achieves above 93% accuracy. The resulting low-dimensional classification model is suitable for embedding into battery-powered systems and for online SOC estimation.

State of Charge Estimation for Lithium-Ion Battery Based on Unscented Kalman Filter and Long Short-Term Memory Neural Network

State of charge (SOC) estimation is the core algorithm of the battery management system. However, the commonly used model-based, data-driven, or experiment-based methods struggle to independently achieve accurate SOC estimation under different working conditions and temperatures, which affects battery performance and safety. To this end, this paper proposes an online SOC estimation method that combines the model-driven and double-data-driven approaches. The unscented Kalman filter (UKF) based on the first-order RC model is used to achieve robust SOC estimation, while the data-driven long short-term memory (LSTM) neural network is used to achieve fast SOC estimation. The former model has an excellent dynamic performance and the latter has high steady-state accuracy. The SOC estimation results are input into the SOC estimation model of series LSTM so that the stable but inaccurate SOC values estimated by UKF in the first part and the accurate but fluctuating SOC values estimated by LSTM can be correlated and corrected, achieving a fast and accurate SOC estimation under various working conditions. The estimation results show that the above method has strong robustness and high accuracy, and effectively reduces model complexity and data redundancy. In addition, the root mean square error of SOC estimation under different working conditions is controlled within 1–2.3% at 0 °C, 25 °C, and 45 °C, which is better than the traditional single-SOC estimation method.

A Systematic and Comparative Study of Distinct Recurrent Neural Networks for Lithium-Ion Battery State-of-Charge Estimation in Electric Vehicles

The precise estimation of the state of charge (SOC) is fundamental to the reliable operation of lithium-ion batteries. The development of deep learning techniques makes it possible to employ advanced methods to estimate a battery’s SOC. In order to better utilize a recurrent neural network (RNN) for battery SOC estimation, this paper conducts a comparative study of SOC estimation methods based on different RNN models. First, a general framework for deep-learning-based SOC estimation is undertaken, followed by the description of four kinds of RNNs employed in the estimation. Then, the estimation performances of these RNN models are compared under three scenarios, including the SOC estimation accuracy, the adaptability against different battery aging statuses, and the robustness against measurement uncertainties, in which the estimation performances of different RNN models are quantitively evaluated. Finally, a multiple-criteria decision-making method based on the analytic hierarchy process (AHP) is utilized to reflect the comprehensive performance of each RNN model, and the model with the highest score could be chosen for online SOC estimation during actual applications. This paper provides an in-depth analysis of RNN models in battery SOC estimation and could help battery management engineers develop the most appropriate estimation methods.

End-Cloud Collaboration Approach for State-of-Charge Estimation in Lithium Batteries Using CNN-LSTM and UKF

The accurate estimation of the state of charge (SOC) plays a crucial role in ensuring the range of electric vehicles (EVs) and the reliability of the EVs battery. However, due to the dynamic working conditions in the implementation of EVs and the limitation of the onboard BMS computational force, it is challenging to achieve a reliable, high-accuracy and real-time online battery SOC estimation under diverse working scenarios. Therefore, this study proposes an end-cloud collaboration approach of lithium-ion batteries online estimate SOC. On the cloud-side, a deep learning model constructed based on CNN-LSTM is deployed, and on the end-side, the coulomb counting method and Kalman’s filter are deployed. The estimation results at both sides are fused through the Kalman filtering algorithm, realizing high-accuracy and real-time online estimation of SOC. The proposed approach is evaluated with three dynamic driving profiles and the results demonstrate the proposed approach has high accuracy under different temperatures and initial errors, where the root means square error (RMSE) is lower than 1.5% and the maximum error is lower than 5%. Furthermore, this method could achieve high-accuracy and real-time SOC online estimation under the cyber hierarchy and interactional network (CHAIN) framework and can be extended to multi-state collaborative online estimation.

Online state of charge estimation for a vanadium redox flow battery with unequal flow rates

This study presents an observer-based methodology to estimate, in real-time, the state of charge of a Vanadium redox flow battery. Different from the available results in the literature, this work presents a new estimator that distinguishes between the concentration in the tank and cell parts of the system. Moreover, it presents an estimation of the state of charge that can deal with both balanced and unbalanced situations. The model used for the observer design is a nonlinear electrochemical model. A nonlinear observer is proposed, designed and validated through simulation and in an experimental prototype.

State of Charge Estimation and Evaluation of Lithium Battery Using Kalman Filter Algorithms.

The accurate and rapid estimation of the state of charge (SOC) is important and difficult in lithium battery management systems. In this paper, an adaptive infinite Kalman filter (AUKF) was used to estimate the state of charge for a 18650 LiNiMnCoO2/graphite lithium-ion battery, and its performance was systematically evaluated under large initial errors, wide temperature ranges, and different drive cycles. In addition, three other Kalman filter algorithms on the predicted SOC of LIB were compared under different work conditions, and the accuracy and convergence time of different models were compared. The results showed that the convergence time of the AUKF algorithms was one order of magnitude smaller than that of the other three methods, and the mean absolute error was only less than 50% of the other methods. The present work can be used to help other researchers select an appropriate strategy for the SOC online estimation of lithium-ion cells under different applicable conditions.

Online Model Parameter and State of Charge Estimation of Li-Ion Battery Using Unscented Kalman Filter Considering Effects of Temperatures and C-Rates

This paper proposed a technique for online modeling and state of charge (SoC) estimation of Li-ion batteries considering the effects of operating temperatures and C-rates. The proposed battery model, which is updated in real-time, is incorporated with the unscented Kalman filter (UKF) for accurate and online SoC estimation. In the proposed technique, Thevenin-based equivalent circuit model of Li-ion battery is used. Each of the RC networks of the Thevenin model is represented as a first-order linear time-invariant (LTI) system. The offline RC parameters are extracted as the parameters of the first-order LTI system using the final value theorem. Then the offline RC parameters are converted to the online model parameters compensating the effects of operating temperatures and C-rates. Finally, the UKF technique is augmented with the proposed online battery model for higher accurate and online SoC estimation. An experimental setup has been developed in the LabVIEW platform to validate the proposed battery model and apply it for online SoC estimation. The proposed online battery model and UKF are developed in Matlab and then integrated with the LabVIEW program using the Matlab-LabVIEW interface called Math Script. The proposed technique has been rigorously validated in the laboratory under hybrid pulse power characterization (HPPC) and federal urban driving schedule (FUDS) tests under wide range of varying operating temperatures and C-rates. In the HPPC test, the SoC estimated using the proposed technique has a maximum absolute relative percentage error (ARPE) of less than 2%, whereas the battery model that does not account for temperature and C-rate effects has a maximum ARPE of 8.79 percent, which is 4.30 times higher than the proposed technique. The proposed approach yielded mean ARPE of 0.30%, 1.02%, and 0.81% in the FUDS test at 25 °C, 0 °C, and 40 °C, respectively, which is performed in dynamic identical C-rates. Furthermore, higher accuracy and effectiveness of the proposed technique have been validated under the presence of white and coloured measurement noises.

Online state of charge and state of power co-estimation of lithium-ion batteries based on fractional-order calculus and model predictive control theory

Accurate battery modelling is the cornerstone to state of charge (SOC) and state of power (SOP) co-estimation of lithium-ion batteries in electric vehicles. Due to strong battery nonlinearity over a broad frequency range, traditional integer-order models are incapable of capturing complex battery dynamics for SOC and SOP co-estimation. This paper proposes a fractional-order modified moving horizon estimation (FO-mMHE) algorithm and a fractional-order model predictive control (FO-MPC) algorithm. Firstly, a second-order FOM is constructed by performing a series of hybrid pulse tests at different SOC regions, and its model parameters are identified through a particle swarm optimization-genetic algorithm method. Secondly, online SOC estimation is converted into a constrained optimization problem in a past moving horizon and then solved by the FO-mMHE algorithm, which enables fast convergence speed and proactive smoothing of estimation outcomes. Thirdly, the FO-MPC algorithm is devised to manipulate the current sequence in a prediction horizon for maximizing discharge/charge power accumulation and determining battery SOP in real time. Moreover, different battery current–voltage behaviors are comprehensively researched in the prediction horizon over a whole battery operating range. The proposed co-estimation method is validated under different dynamic load profiles. The experimental results demonstrate a SOC estimation error reduction of up to 1.2 % compared with the commonly used fractional-order extended Kalman filter while the SOP estimation error could be limited below 0.35 W.

A Multi-Scale Time Method for the State of Charge and Parameter Estimation of Lithium-Ion Batteries Using MIUKF-EKF

Accurate state estimation is essential for the safe and reliable operation of lithium-ion batteries. However, the accuracy of the battery state estimation depends on the accuracy of the battery parameters. Because the state of charge (SOC) cannot be directly measured, estimation methods based on the Kalman filter are widely used. However, it is difficult to estimate SOC online and get high accuracy results. This article proposes a method for parameter identification and SOC estimation for lithium-ion batteries. Because the lithium-ion battery has slow-varying parameters (such as internal resistance, and polarization resistance), and the SOC has fast-varying characteristics, so a multi-scale multi-innovation unscented Kalman filter and extended Kalman filter (MIUKF-EKF) are used to perform online measurement of battery parameters and SOC estimation in this method. The battery parameters are estimated with a macro-scale, and the SOC is estimated with a micro-scale. This method can improve the estimation accuracy of the SOC in real-time. Results of experiments indicate that the algorithm has higher accuracy in online parameter identification and SOC estimation than in the dual extended Kalman filter (DEKF) algorithm.

A Comparative Study on Different Online State of Charge Estimation Algorithms for Lithium-Ion Batteries

With an accurate state of charge (SOC) estimation, lithium-ion batteries (LIBs) can be protected from overcharge, deep discharge, and thermal runaway. However, selecting appropriate algorithms to maintain the trade-off between accuracy and computational efficiency is challenging, especially under dynamic load profiles such as electric vehicles. In this study, seven different widely utilized online SOC estimation algorithms were considered with the following goals: (a) to compare the accuracy of the different algorithms; (b) to compare the computational time in the simulation. Since the 2-RC battery model is highly accurate and not very computationally complex, it was selected for implementing the considered algorithms for the model-based SOC estimation. The considered online SOC estimation performance was evaluated using measurement data obtained from experimental tests on commercial lithium manganese cobalt oxide batteries. The experimental analysis consisted of a dynamic current profile comprising a worldwide harmonized light vehicle test procedure (WLTP) cycle and constant current discharging pulses. In addition, the performance of the considered different algorithms was compared in terms of estimation error and computational time to understand the challenges of each algorithm. The results indicated that the extended Kalman filter (EKF) and sliding mode observer (SMO) were the best choices because of their estimation accuracy and computation time. However, achieving the SOC estimation accuracy depended on the battery modeling. On the other hand, the estimated SOC root means square error (RMSE) using a backpropagation neural network (BPNN) was less than that using a Luenberger observer (LO). Moreover, with the advantages of BPNNs, such as no need for battery modeling, the estimation error could be further reduced using a large size dataset.

Real-time state of charge estimation for electric vehicle power batteries using optimized filter

The main focus of the battery management system is the estimation of the battery's State of Charge (SOC), which is an indicator to determine the driving range of an electric vehicle. The Extended Kalman Filter (EKF) algorithm is the most promising for SOC estimation when the system is running. The EKF state estimation algorithm is sensitive to the process noise covariance matrix Q and measurement noise covariance matrix R. Inappropriate noise covariance matrices reduce the accuracy and cause divergence in state estimation. This paper uses the Sunflower Optimization algorithm (SFO) to find the optimal values of the noise covariance matrices before applying EKF for online SOC estimation. It is clearly stated that the iterative SFO does not affect the instantaneous response of EKF in the online estimate because the SFO is only performed once to determine the optimal values. The effectiveness of the proposed identification is examined through the constant discharge rate test and dynamic driving profile. The proposed algorithm's performance indices, such as maximum error, Mean Absolute Error, Mean Square Error, and Root Mean Square Error of SOC estimation, are low compared to the trial-error method, genetic algorithm, and adaptive extended Kalman filter. Besides accuracy, the proposed method quickly converges even when the initial SOC is inaccurate. The feasibility and benefits of the proposed SFO-EKF algorithm are demonstrated by qualitative and quantitative findings on five challenging datasets. To assess the performance of the SFO-EKF for SOC estimation in constant-current discharge and extreme drive cycle situations, three public datasets and two datasheets are employed. The simulation results show that the proposed method has high accuracy and a better convergence rate in estimating SOC under static and dynamic operating conditions.

All-climate state-of-charge estimation and equilibrium management for lithium-ion batteries based on diffusion equivalent model

All-climate application of lithium-ion batteries is of crucial importance for future promotion on transportation and energy storage, which is still suffering from the unprecise model and algorithms. In this article, a coupled diffusion-equivalent circuit model is proposed for solving the problems of all-climate and multi-conditional battery modeling, which is developed based on simplified electrochemical theories. And the simplex sphere-radial particle filter is introduced for delivering the precise method on the estimation for state of charge according to rigorous mathematical demonstration. Moreover, the equilibrium system is established based on original battery management system, and both cell-level and module-level experiments are carried out for validating the effectiveness and precision of proposed method. Maximum error of no more than 3% can be observed both for all-climate (between −20 °C–45 °C) and large depth of discharging, and 1% inconsistency can be achieved within sufficient balancing. The satisfactory results confirm that the proposed method can perform an accurate and robust solution for online state of charge estimation, and deliver great potential on future promotion for energy storage system or remote cloud-controlling system.

An adaptive state of charge estimator for lithium‐ion batteries

AbstractThis study presents a data‐driven approach in conjunction with an adaptive extended Kalman filter (AEKF) to estimate lithium‐ion batteries' state of charge (SOC) online. The Thevenin battery model is used to evaluate the effects using battery voltage and current. The advantages of the Lagrange multiplier method are utilized to model the lithium‐ion battery. The Lagrange multiplier method continuously decreases the model error to adjust the Kalman gain of AEKF for accurate SOC estimation. Various current profiles such as hybrid pulse test, dynamic stress test, and Beijing dynamic stress test are used to verify the proposed approach's adaptability, robustness, and accuracy. It is observed that the proposed approach outperforms other methodologies (recursive least square–AEKF and forgetting factor recursive least square–AEKF) due to its high accuracy (mean average error of 0.32%). Additionally, the proposed approach exhibits robustness and high convergence speed despite deliberate erroneous initialization of parameters, thus indicating its applicability in online SOC estimation applications.

On-line WSN SoC estimation using Gaussian Process Regression: An Adaptive Machine Learning Approach

Wireless sensor networks (WSN) are low-resource devices that run on small batteries. The availability of battery energy, device drive cycles, and environmental conditions all have an impact on node lifetime. The state of charge (SoC) is an important factor in determining the amount of energy available in the batteries. Accurate SoC estimation is critical for device lifetime prediction and safe device operation. We present a novel approach for adaptive SoC estimation based on Gaussian Process Regression in this paper (GPR). The training data was obtained in a climate-controlled laboratory setting by using IEEE 802.15.4-based drive loads at various temperatures for three different batteries such as Lithium-Ion, Nickel-metal hydride, and Lithium-Polymer. To estimate the SoC, battery parameters such as voltage, capacity, and temperature were directly mapped to the corresponding models. For each battery parameter, the GPR model with hyper tuned Radial Bias Filter (RBF) was trained at temperatures ranging from 5 °C to 45 °C. For model accuracy, the proposed scheme was compared to polynomial regression and support vector machines (SVM). In this regard, the proposed model provided Mean Absolute Error (MAE) values of 2.53 percent, 2.54 percent, and 2 percent, respectively, and Root Mean Square Error (RMSE) values of 0.295, 0.292, and 0.35 for Nickel-metal hydride, Lithium-Polymer, and Lithium-Ion batteries at 25 °C. Our proposed lightweight GPR scheme is, to the best of our knowledge, the only active implementation on embedded platforms for SoC estimation of WSN. Finally, the model was rigorously tested on ARM Cortex M4-based microcontrollers to report real-time online SoC estimation on WSN nodes.

A Hierarchical Approach for Finite-Time H-$\infty$ State-of-Charge Observer and Probabilistic Lifetime Prediction of Lithium-Ion Batteries

Accurate state-of-charge (SOC) estimation and lifetime prognosis of lithium-ion batteries are of great significance for reliable operations of energy storage systems. This paper proposes a novel two-layer hierarchical approach for online SOC estimation and remaining-useful-life (RUL) prediction based on a robust observer and Gaussian-process-regression (GPR). At the bottom layer, an equivalent-circuit model is first developed to describe battery dynamics. Second, a combination method of a recursive least square method and a finite time H- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\infty$</tex-math></inline-formula> observer is designed to estimate battery open-circuit-voltage (OCV) and SOC through stability and robustness analysis. Next, the estimated OCV and SOC are fed into the top layer to generate the incremental-capacity-analysis-based aging feature, through which a robust signature associated with battery aging is identified. The feature is further employed for RUL prediction based on GPR. The salient advantages of the proposed approach are that it can provide robust parameter estimation in a given finite-time interval, and the GPR-based RUL prediction can tackle long-term uncertainties in a principled Bayesian manner. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed SOC observer and lifetime prediction methods.

A computationally efficient adaptive online state-of-charge observer for Lithium-ion battery for electric vehicle

Due to the large number of cells installed in electric vehicle (EV), its battery management system (BMS) requires efficient state of charge (SOC) estimation algorithm. Since there is an impetus to reduce the computational burden (while retaining an acceptable accuracy), this paper proposes a simple and fast online adaptive observer for SOC estimation of Lithium-ion battery. The observer has several attractive features: first, its stability is proven by Lyapunov approach where asymptotic error convergence is guaranteed. Second, the computational requirements are low since it contains a few simple recursive equations without matrix inversion. Third, it is adaptive and achieves simultaneous online estimation of SOC and most of the battery parameters. The practical implementation using a 3 Ah battery proves the effectiveness of the proposed observer under dynamic stress test (DST). The testing with real EV profiles (supplemental federal test procedure which is known as US06 and federal urban driving schedule FUDS) is also performed to show the reliability. It is confirmed that the computation time of the proposed algorithm is reduced by approximately 2.5 times in compared to the extended Kalman filter-recursive least square (EKF-RLS) method. Despite the reduction in computation time, the errors are comparable to the latter. The low computational cost is significant when considering the need to accurately estimate the SOC of a large number of cells in a battery pack of an EV.

Deep learning enabled state-of-charge estimation of LiFePO4 batteries: A systematic validation on state-of-the-art charging protocols

LiFePO4 batteries generally face a challenge of inaccurate state of charge (SoC) estimation due to the plateaus existing in the middle range of the open circuit voltage (OCV)-SoC curve. Generally, conventional SoC estimation methods are not capable of accurately estimating the SoC in this range. In this paper, a deep neural network (DNN) is constructed to estimate the SoC in the charging process. Battery data collected from five state-of-the-art charging protocols at 10 °C, 25 °C and 40 °C are used to train the DNN. The developed DNN can be used for online SoC estimation subsequently. This estimated SoC can serve as the initial SoC of the ampere-hour counting method to calculate the SoC of the discharging process. The overall maximum error and the root mean square error of the SoC estimation over charging process are within 2.5% and 0.8%, respectively. In addition, the input depth of time from 10 s to 100 s with a 10 s interval is investigated. The maximum error is less than 5% in the case of the depth time within 100 s and the error fall to 2% when the depth of time reaches 90 s.