Online State Of Charge Research Articles

Adaptive optimal observer for real-time state of charge estimation of lithium-ion batteries in robotic systems

PurposeThis study aims to address the challenge of the real-time state of charge (SOC) estimation for lithium-ion batteries in robotic systems, which is critical for monitoring remaining battery power, planning task execution, conserving energy and extending battery lifespan.Design/methodology/approachThe authors introduced an optimal observer based on adaptive dynamic programming for online SOC estimation, leveraging a second-order resistor–capacitor model for the battery. The model parameters were determined by fitting an exponential function to the voltage response from pulse current discharges, and the observer's effectiveness was verified through extensive experimentation.FindingsThe proposed optimal observer demonstrated significant improvements in SOC estimation accuracy, robustness and real-time performance, outperforming traditional methods by minimizing estimation errors and eliminating the need for iterative steps in the adaptive critic and actor updates.Originality/valueThis study contributes a novel approach to SOC estimation using an optimal observer that optimizes the observer design by minimizing estimation errors. This method enhances the robustness of SOC estimation against observation errors and uncertainties in battery behavior, representing a significant advancement in battery management technology for robotic applications.

Modeling and SOC estimation of on-board energy storage device for trains under emergency traction

The sudden interruption of train power supply in an extreme environment will seriously threaten the safety of passengers and affect the operational efficiency of the railway system. In this case, the focus of attention becomes a method of running the train to the nearest rescue point based on the limited capacity of the on-board emergency energy storage device. Therefore, this paper reports research on the state of charge (SOC) estimation of train energy storage equipment to optimize the emergency traction strategy and energy utilization rate of trains to the maximum extent. First, with the emergency power supply of on-board lithium titanate batteries, the energy flow model of train emergency power supply is constructed for the first time. Second, based on the second-order equivalent circuit model and considering the utilization of regenerative braking energy, the relationship between battery capacity and open circuit voltage (OCV), temperature, current and SOC are constructed through experimental data, which significantly improves the accuracy and robustness of SOC estimation in complex and variable environments. Then, to effectively eliminate the impact of environmental on the estimation especially in the case of extremely low temperature (−20 °C), online model parameter discrimination and SOC estimation of lithium batteries are realized by combining recursive least squares with an optimal forgetting factor (FRLS) algorithm and a new temperature forgetting factor based adaptive extended Kalman filter (TFFAEKF) algorithm. The experimental results show that the proposed method achieves accurate SOC estimation, and the maximum error is less than 1% at different temperatures.

A new online SOC estimation method using broad learning system and adaptive unscented Kalman filter algorithm

The accurate estimation of lithium batteries’ state of charge (SOC) is important for extending battery life and preventing accidents. To improve the battery model’s adaptability to variations in actual operating conditions, this paper proposes a new hybrid SOC estimation method. The battery model is first built based on the broad learning system (BLS) to simulate the battery’s voltage characteristics. Subsequently, the adaptive unscented Kalman filter algorithm is applied for SOC estimation. We introduce the Bernstein inequality (BI) to guide the BLS model’s online update process. With the BI method, the redundant incremental data is not used for battery model updates, which improves the model’s online learning efficiency. Finally, dynamic test operation data is collected from different temperatures to validate the proposed SOC estimation algorithm. Experimental results manifest that the SOC estimation error can be limited to 0.51 %. In addition, the proposed method has satisfactory training and online learning time consumption.

Online state of charge estimation of LiFePO4 battery based on EKF-AUKF algorithm with reference compensation for estimation results

The state of charge(SOC) is an important index in Battery Management System(BMS) for smart grids and electric vehicles, whose accuracy is affected by model and sensor errors. In this paper, an online SOC estimation method based on EKF-AUKF algorithm with reference compensation for estimation results is proposed. Firstly, a joint estimation method based on extended Kalman filter(EKF) and adaptive unscented Kalman filter(AUKF) algorithm is adopted to estimate SOC under Beijing bus dynamic stress test(BBDST) condition. The result shows that the estimation error is within 2 %. Secondly, the characteristics of EKF-AUKF algorithm under voltage and current sampling errors are analyzed over the whole SOC range. The results indicate that voltage measurement error increases SOC estimation error. Then, an online reference is built by calculating the sum of the estimation result of ampere-hour counting(AHC) method and constant deviation, and then the difference between the estimation result of EKF-AUKF algorithm and online reference can be obtained. The absolute value of the difference is used to compare with limit deviation value and compensate the SOC of EKF-AUKF method by different compensation coefficients. Finally, the effectiveness of the proposed method is verified under different operating conditions. The experimental results show that the proposed method can greatly improve the SOC estimation accuracy under large voltage error.

Target decomposition-led light-weighted offline training strategy-aided data-driven state-of-charge online estimation during constant current charging conditions over battery entire lifespan

This paper develops a novel target decomposition-led light-weighted offline training strategy-aided data-driven state-of-charge (SOC) online estimation method during constant current (CC) charging conditions over battery entire lifespan. Firstly, real SOC is conceptually decomposed into base SOC and SOC error. Subsequently, taking voltage and real SOC of initial CC charging cycle as input and output, machine learning algorithm is adopted to offline establish base SOC acquisition model without considering battery aging. Thirdly, the errors between real SOC and acquired base SOC are calculated, where the extremely similar distribution of SOC error against different battery degradation with two aging-dependent peaks can be clearly observed. Following this precious characteristic, a SOC error calculation model is further built only via several typical CC charging cycles with base SOC and battery capacity as input. Finally, the acquired base SOC is compensated by the computed SOC error for real SOC calculation. The validation results demonstrate that the proposed target decomposition-led method has overwhelming advantages in light-weighted offline training and accurate SOC online estimation during CC charging conditions, where maximum mean absolute error and maximum root mean squared error of SOC estimation results over the same type of batteries’ entire lifespan are only 0.98 % and 1.2 %, respectively.

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%.

Battery state of charge estimation solution based on optimized Ah counting and online calibration strategy for electric vehicle

Abstract State of charge (SOC) estimation is critical for electric vehicles (EVs); the typical solution is the ampere-hour (Ah) counting strategy + open circuit voltage (OCV) strategy as they are straightforward and easy to implement. However, this solution makes a significant SOC estimation error if the driver needs to drive long distances or in winter. This article aims to optimize the Ah counting strategy and propose an online SOC calibration strategy. For the former, we evaluate the effects of temperature, initial SOC, and current on the Coulomb efficiency and the impact of temperature and discharge current on the battery capacity and take them into account when estimating the battery SOC; for the latter, we conduct theoretical analysis and argue that after a while of small-current fluctuations in the battery, the OCV of the battery can be obtained based on the battery voltage, current, and direct current (DC) resistance, and can be calibrated online. We designed experiments to validate the proposed strategy. The experimental results show that the optimized Ah counting strategy does not pull away from the standard Ah counting strategy at room temperature or high temperature, which is because the effects of the Coulombic efficiency and the battery capacity can be canceled out, but the optimized Ah counting strategy has a better performance at low temperature, and vice versa for standard Ah counting performs poorly; for SOC online calibration, the OCV estimated online by the proposed strategy differs from the reference OCV by only 2 mV, and its performance is excellent. The solution proposed in this article can be applied to EVs to obtain better performance.

A totally coupled multi time-scale framework containing full parameters online identification and SOC real-time estimation of lithium-ion battery based on a fractional order model

Fractional order model (FOM) is one of the most promising choices for lithium-ion battery simulation and internal states estimation due to its high modeling accuracy. However, online identifying the order and parameters of FOM is extremely tough, which also makes it difficult to be applied in complex and variable operating conditions. To address this issue, this paper proposes a totally coupled multi time-scale framework that contains full parameters online identification of FOM and state-of-charge (SOC) real-time estimation of lithium-ion battery. Firstly, a novel global optimization algorithm named improved particle swarm optimization is designed to update the order of FOM on macro-time scale with low computational burden. On the basis of the determined order, the rest parameters of FOM are further identified by forgetting factor recursive least square algorithm on micro-time scale. With those online identified parameters, adaptive extended Kalman filter is finally adopted to track battery SOC in every instant. The estimation accuracy, adaptability to different operating temperatures and battery aging, and robustness ability against uncertain initialization of the developed method is verified under Federal Urban Driving Schedule tests. The corresponding results demonstrate that the proposed method can realize accurate full parameters online identification of FOM and precise SOC real-time estimation against different temperatures, battery aging states and initialization. Using the developed method, the mean absolute error (MAE) and root mean square error (RMSE) of SOC estimation of the fresh battery under temperature ranging from 0 °C to 50 °C can be limited below 0.9 % and 1.1 %, respectively. Even if the SOC-OCV relationship is not timely updated, those two indexes of the aged battery achieved by the proposed method can still be controlled within 3 % under temperature ranging from 0 °C to 50 °C. Moreover, the comparison with other typical FOM-based estimation methods is also conducted, whose results indicate that the developed method has apparently superior comprehensive performance on estimation accuracy and adaptation.

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.

SOC estimation of retired lithium-ion batteries for electric vehicle with improved particle filter by H-infinity filter

The echelon utilization of retired lithium-ion battery with remaining capacity of 80%, is considered as one of the most promising ways to reduce battery cost by extending their service life. The accurate state of charge (SOC) estimation for retired lithium-ion batteries is of great significance for less-stressful demanding applications. The H-infinity filter (HIF) is widely used to identify the battery model parameters and correspondingly to estimate the SOC online assisted with the Thevenin model. But the estimation accuracy cannot be ensured due to the overly simple algorithm structure. In this paper, H-infinity particle filter (HIPF) is proposed to further improve the SOC estimation accuracy. It is a particle filter (PF) improved by HIF and can suppress the particle depletion during the execution of the standard particle filter. HIPF estimated the SOC after the weights of particles were compromised. The joint estimation of model parameters by HIF and the SOC by HIPF was simulated to verify the model accuracy. In the experiment, the retired lithium–iron phosphate battery in BAIC EV150 vehicle was tested under FUDS cycle and DST cycle. The verification result shows that the mean error of the estimated SOC by HIPF is 0.63% in FUDS cycle and 0.59% in DST cycle. And in FUDS cycle and DST cycle, respectively, the proposed method’s SOC estimation accuracy was increased by 65% and 63% compared with when particle weights were not compromised.

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 Dual-Input Neural Network for Online State-of-Charge Estimation of the Lithium-Ion Battery throughout Its Lifetime.

Online state-of-charge (SOC) estimation for lithium-ion batteries is one of the most important tasks of the battery management system in ensuring its operation safety and reliability. Due to the advantages of learning the long-term dependencies in between the sequential data, recurrent neural networks (RNNs) have been developed and have shown their superiority over SOC estimation. However, only time-series measurements (e.g., voltage and current) are taken as inputs in these RNNs. Considering that the mapping relationship between the SOC and the time-series measurements evolves along with the battery degradation, there still remains a challenge for RNNs to estimate the SOC accurately throughout the battery’s lifetime. In this paper, a dual-input neural network combining gated recurring unit (GRU) layers and fully connected layers (acronymized as a DIGF network) is developed to overcome the above-mentioned challenge. Its most important characteristic is the adoption of the state of health (SOH) of the battery as the network input, in addition to time-series measurements. According to the experimental data from a batch of LiCoO2 batteries, it is validated that the proposed DIGF network is capable of providing more accurate SOC estimations throughout the battery’s lifetime compared to the existing RNN counterparts. Moreover, it also shows greater robustness against different initial SOCs, making it more applicable for online SOC estimations in practical situations. Based on these verification results, it is concluded that the proposed DIGF network is feasible for estimating the battery’s SOC accurately throughout the battery’s lifetime against varying initial SOCs.

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.

Joint Estimation of SOC and SOH for Single-Flow Zinc–Nickel Batteries

The single-flow zinc–nickel battery (ZNB) is a new type of flow battery with a simple structure, large-scale energy storage, and low cost, and thus has attracted much attention in the battery field recently. The state of charge (SOC) and state of health (SOH) are key indicators of the battery, and their inaccurate estimation can damage the battery. However, little has been done so far to study how to jointly estimate SOC and SOH for the ZNB. In this paper, the method of adaptive IDUKF is proposed. A second-order equivalent circuit model is applied to improve the accuracy. At the same time, the double unscented Kalman filter (DUKF), which is optimized by the improved Harris hawk optimization (IHHO) algorithm, is used to estimate the SOC and parameters online. Then, the capacity update model is introduced to simulate the change in SOH. Finally, the proposed method is applied to a 16 Ah ZNB, and the experimental results confirm the validity of the proposed method.