Model-based State Of Charge Estimation Research Articles

Impact of Data Corruption and Operating Temperature on Performance of Model-Based SoC Estimation

Electric vehicles (EVs) are becoming popular around the world. Making a lithium battery (LIB) pack with a robust battery management system (BMS) for an EV to operate under different complex environments is both a challenge and a requirement for engineers. A BMS can intelligently manage LIB systems by estimating the battery state of charge (SoC). Due to the nonlinear characteristics of LIB, influenced by factors such as the harsh environment and data corruption caused by electromagnetic interference (EMI) inside electric vehicles, SoC estimation should consider available capacity, model parameters, operating temperature and reductions in data sampling time. The widely used model-based algorithms, such as the extended Kalman filter (EKF) have limitations. Therefore, a detailed review of the balance between temperature, data sampling time, and different model-based algorithms is necessary. Firstly, a state of charge—open-circuit voltage (SoC-OCV) curve of LIB is obtained by the polynomial curve fitting (PCF) method. Secondly, a first-order RC (1-RC) equivalent circuit model (ECM) is applied to identify the battery parameters using a forgetting factor-based recursive least squares algorithm (FF-RLS), ensuring accurate internal battery parameters for the next step of SoC estimation. Thirdly, different model-based algorithms are utilized to estimate the SoC of LIB under various operating temperatures and data sampling times. Finally, the experimental data by dynamic stress test (DST) is collected at temperatures of 10 °C, 25 °C, and 40 °C, respectively, to verify and analyze the impact of operating temperature and data sampling time to provide a practical reference for the SoC estimation.

An electrochemical-thermal coupling model for lithium-ion battery state-of-charge estimation with improve dual particle filter framework

Lithium-ion battery state-of-charge (SOC) estimation plays an indispensable role in the battery management system functionalities. To achieve SOC estimation with high accuracy, a precise battery model is required. Among various battery models, electrochemical model (EM) stands out for its ability to provide insights into the electrochemical mechanisms of the battery. However, the model parameters will vary with the battery running and aging, besides, the model-based methods cannot well handle the model errors. Therefore, to ensure estimation accuracy, selecting a more insightful battery model and a more effective estimation algorithm becomes crucial. This paper proposes an electrochemical model-based SOC estimation method with online parameter adjustment and an optimized algorithm. Firstly, a single particle model (SPM) with electrolyte and thermal dynamics is introduced and simplified by an approximate solution. Secondly, the particle swarm optimization (PSO) method is used to solve the problem of the particle filter (PF) algorithm, such as particle degradation and particle diversity decrease. Finally, during SOC estimating, a double-scale dual particle filter (D-PF) is utilized to adjust parameters as battery aging and temperature changes. The battery tests are applied under different working conditions and temperatures. Experimental results show that the error of SOC estimation reduces significantly compared to the previous electrochemical model-based method, and the proposed method has a higher accuracy and effectiveness.

Robust state-of-charge estimation for LiFePO4 batteries under wide varying temperature environments

During the driving process of electric vehicles, the ambient temperature exhibits diverse variations with regional characteristics. To achieve robust state of charge (SOC) estimation for lithium-ion batteries under various varying temperature environments, this paper proposes an enhanced model-based closed-loop SOC estimation approach. First, beginning with a mechanistic analysis of batteries, the traditional second-order equivalent circuit model is enhanced by incorporating critical solid-phase diffusion effects during battery operation. Furthermore, utilizing data collected from multiple constant temperature environments, the complete enhanced battery model that accounts for the influence of current rates across a wide temperature range is constructed. Subsequently, under environments of different varying temperature settings, we design a series of complex operation experiments to verify the accuracy and generalizability of the established battery model. Meanwhile, a high-performance adaptive diagonalization of matrix cubature Kalman filter is introduced to address the challenge of fluctuating sampling noises in battery operation. Finally, the robustness and generalization of the proposed SOC estimation method are verified in multiple complex operating experiments under varying temperatures with non-Gaussian noise interferences and with non-full charging schemes. Remarkably, the proposed approach consistently delivers high-precision SOC estimation results across all scenarios, maintaining root mean square error and mean absolute error below 1.5%.

An Adaptive Extended Kalman Filter for Model-Based Fault Diagnosis and State of Charge Estimation of Lithium-Ion Batteries

Precisely gauging the state of charge (SOC) of a lithium-ion battery poses a considerable obstacle due to the battery's intricate electrochemical properties, which are highly dynamic and nonlinear. The effectiveness of the control strategy employed in electric vehicles heavily hinges on the precise estimation of the battery's SOC. Among the crucial elements, the accurate assessment of SOC for power lithium-ion batteries stands out. Ensuring the durability and reliability of battery management systems in electric vehicles to predict SOC is a multifaceted endeavor. Given the inherently nonlinear degradation pattern of batteries, achieving precise forecasting of SOC while minimizing degradation proves to be a demanding task. The accurate determination of battery SOC holds significant significance for both battery electric vehicles and hybrid electric vehicles. Lithium-ion batteries have gained extensive usage in various facets of daily life due to their positive environmental and resource-related attributes. The precise determination of SOC is pivotal in ensuring proper battery operation. Nonetheless, the challenges of SOC estimation under low temperatures have received limited attention. To tackle this issue, this study introduces an adaptive extended Kalman Filter for model-based fault diagnosis and SOC estimation of lithium-ion batteries.

Dynamic ultrasonic response modeling and accurate state of charge estimation for lithium ion batteries under various load profiles and temperatures

Accurate estimation of the State of Charge (SoC) plays a vital role in ensuring the efficient and safe operation of lithium iron phosphate (LFP) batteries. However, the flat open circuit voltage (OCV) curve of the LFP battery implies a low sensitivity to SoC, which results in large SoC estimation errors in the presence of noisy terminal voltage measurements. To address this challenge, an SoC estimation methodology utilizing an ultrasonic reflection response model is proposed, which is the first methodology regarding highly accurate and robust ultrasonic model-based SoC estimation under dynamic load profiles. Since ultrasound waves enable non-destructive acquisition of battery internal physical property changes directly associated with SoC, the ultrasonic battery near-surface reflection feature is extracted and demonstrated to exhibit a highly linear correlation with and higher sensitivity to SoC. We pioneeringly construct an empirical differential ultrasonic model to describe how the ultrasonic feature depends on the SoC and dynamic current. The advantage of such an ultrasonic model is demonstrated by theoretical and experimental results of an Adaptive Extend Kalman Filter (AEKF) and an Adaptive H-infinity Filter (AHIF) under various dynamic load profiles and temperatures. The Root Mean Square Error (RMSE) for ultrasonic model-based SoC estimation remains at approximately 1% across all tests, reducing by 36.7% compared to the voltage model, which shows its great potential in accurate SoC estimation.

Model-Based State-of-Charge and State-of-Health Estimation Algorithms Utilizing a New Free Lithium-Ion Battery Cell Dataset for Benchmarking Purposes

State estimation for lithium-ion battery cells has been the topic of many publications concerning the different states of a battery cell. They often focus on a battery cell’s state of charge (SOC) or state of health (SOH). Therefore, this paper introduces, on the one hand, a new lithium-ion battery dataset with dynamic validation data over degradation and, on the other hand, a model-based SOC and SOH estimation based on this dataset as a reference. An unscented Kalman-filter-based approach was used for SOC estimation and extended with a holistic ageing model to handle the SOH estimation. The paper describes the dataset, the models, the parameterisation, the implementation of the state estimations, and their validation using parts of the dataset, resulting in SOC and SOH estimations over the entire battery life. The results show that the dataset can be used to extract parameters, design models based on it, and validate it with dynamically degraded battery cells. The work provides an approach and dataset for better performance evaluations, applicability, and reliability investigations.

ANN-based State of Charge Estimation of Li-ion Batteries for Embedded Applications

The conventional state of charge (SOC) estimation model has several concerns, such as accuracy and reliability. In order to realize robust SOC estimation for embedded applications, this study focuses on three concerns of the existing SOC estimation model: accuracy, robustness, and practicality. In improving the estimation accuracy and robustness, this study took into account the dynamic of the actual SOC caused by the dynamic charging and discharging process. In practice, the charging and discharging processes have characteristics that must be considered to realize robust SOC estimation. The model-based SOC estimation developed based on the virtual battery model causes difficulties for real-time applications. Additionally, model-based SOC estimation cannot be reliably extrapolated to different battery types. In defining the behavior of various types of batteries, the model-based SOC estimation must be updated. Hence, this study utilized data-driven SOC estimation based on an artificial neural network (ANN) and measurable battery data. The ANN model, which has excellent adaptability to nonlinear systems, is utilized to increase accuracy. Additionally, using measurable battery data such as voltage and current signals, the SOC estimation model is suitable for embedded applications. Results indicate that estimating SOC with the proposed model reduced errors with respect to actual datasets. In order to verify the feasibility of the proposed model, an online estimation was out on the embedded system with the use of C2000 real-time microcontrollers. Results show that the proposed model can be executed in an embedded system using measurable battery data.

Lithium-Ion Battery State-of-Charge Estimation Using Electrochemical Model with Sensitive Parameters Adjustment

State-of-charge (SOC) estimation of lithium-ion (Li-ion) batteries with good accuracy is of critical importance for battery management systems. For the model-based methods, the electrochemical model has been widely used due to its accuracy and ability to describe the internal behaviors of the battery. However, the uncertainty of parameters and the lack of correction from voltage also induce errors during long-time calculation. This paper proposes a particle filter (PF) based method to estimate Li-ion batteries’ SOC using electrochemical model, with sensitive parameter identification achieved using the particle swarm optimization (PSO) algorithm. First, a single particle model with electrolyte dynamics (SPME) is used in this work to reduce the computational burden of the battery electrochemical model, whose sensitive parameters are selected through the elementary effect test. Then, the representative sensitive parameters, which are difficult to measure directly, are adjusted by PSO for a high efficiency. Finally, a model-based SOC estimation framework is constructed with PF to achieve accurate Li-ion battery SOC. Compared with extended Kalman filter and equivalent circuit model, the proposed method shows high accuracy under three different driving cycles.

Evaluation of Various Offline and Online ECM Parameter Identification Methods of Lithium-Ion Batteries in Underwater Vehicles.

For underwater vehicles, the state of charge (SOC) of battery is often used to guide the optimal allocation of energy. An accurate SOC estimation can improve work efficiency and reliability of underwater vehicles. Model-based SOC estimation methods are still mainstream routes used in practical applications. Hence, accurate battery models are highly desirable, which depends not only on the circuit structure but also on the circuit parameters. Four-parameter identification algorithms, offline mechanism-based and least squared (LS) methods, as well as online recursive least-squares with forget factor (FFRLS) and extended Kalman filter (EKF) methods were analyzed in terms of SOC estimation under three different conditions. The results revealed that in the case without any disturbance, the predicted SOCs based on four-parameter identification circuits fitted well with the reference. Moreover, it is remarkable that the LS offline methods work better than the FFRLS online routes. In addition, the robustness has also been accessed through the other two conditions, i.e., measurement data with disturbance and initial SOC value with deviation. The results showed that maximum errors of SOC estimation based on the EKF approach are significantly lower than those of the other methods, and the values are 0.51% and 0.20%, respectively. Thus, the circuit model based on the EKF parameter identification approach possessed a stronger anti-interference performance during the SOC estimation process. This research can provide corresponding theoretical support on ECM parameter identification for lithium-ion batteries in underwater vehicles.

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.

State-of-charge estimation with adaptive extended Kalman filter and extended stochastic gradient algorithm for lithium-ion batteries

Online state-of-charge (SOC) estimation is a critical element for battery management systems and it requires lower computing cost and acceptable range of accuracy. This paper proposes a new model-based SOC estimation method for lithium-ion batteries. By utilizing the state estimation to identify the model parameters and then re-estimate the state by using the identified parameters, the two steps of parameter identification and state estimation are integrated into one closed-loop algorithm and they are implemented by using extended stochastic gradient (ESG) algorithm and adaptive extended Kalman filter (AEKF), respectively. In this method, it is unnecessary to calculate each circuit parameter of the model separately resulting in simper structure and lower computing cost. Experimental results indicate that the proposed SOC estimation algorithm has good performance in terms of estimation accuracy and robustness under different test conditions. It is therefore more suitable for online SOC estimation of lithium-ion batteries.

Online Parameters Identification and State of Charge Estimation for Lithium-Ion Battery Using Adaptive Cubature Kalman Filter

The state of charge (SOC) of a lithium-ion battery plays a key role in ensuring the charge and discharge energy control strategy, and SOC estimation is the core part of the battery management system for safe and efficient driving of electric vehicles. In this paper, a model-based SOC estimation strategy based on the Adaptive Cubature Kalman filter (ACKF) is studied for lithium-ion batteries. In the present study, the dual polarization (DP) model is employed for SOC estimation and the vector forgetting factor recursive least squares (VRLS) method is utilized for model parameter online identification. The ACKF is then designed to estimate the battery’s SOC. Finally, the Urban Dynamometer Driving Schedule and Dynamic Stress Test are utilized to evaluate the performance of the proposed method by comparing with results obtained using the extended Kalman filter (EKF) and the cubature Kalman filter (CKF) algorithms. The simulation and experimental results show that the proposed ACKF algorithm combined with VRLS-based model identification is a promising SOC estimation approach. The proposed algorithm is found to provide more accurate SOC estimation with satisfying stability than the extended EKF and CKF algorithms.

A comparative study of the influence of different open circuit voltage tests on model‐based state of charge estimation for lithium‐ion batteries

A predetermined relationship between open circuit voltage (OCV) and state of charge (SoC) is the premise of model-based SoC estimation algorithms. Commonly used OCV tests to obtain the offline OCV-SoC curves include the low current OCV test and the incremental OCV test. In this paper, in addition to comparing the low current OCV test with the incremental OCV test which applies 0.5 C current-rate, the incremental OCV tests which apply 0.2, 0.3, and 1 C current-rates are compared as well. Moreover, from the perspective of test accuracy and test duration, the optimal relaxation time for incremental OCV test is investigated. The recursive least squares method with a forgetting factor (FFRLS) is used to identify the parameters of the battery model, and the adaptive extended Kalman filter (AEKF) is employed to estimate SoC. The results indicate that the SoC estimator which applies the OCV-SoC curve obtained from the 0.5 C incremental OCV test performs better than other estimators at 25°C and 45°C. But at 0°C, the SoC estimator which applies the OCV-SoC curve obtained from the 0.2 C incremental OCV test has the best estimation performance. In addition, 3 h relaxation time is the optimal choice at 25°C and 45°C, while 4 h relaxation time is recommended at 0°C.

Electrochemical-distributed thermal coupled model-based state of charge estimation for cylindrical lithium-ion batteries

State of Charge (SoC) is essential in a smart Battery Management System (BMS). Traditional SoC estimation methods consider the lithium battery cell as an isothermal body simplistically, which is not accurate. Due to the heat conduction and convection, the temperature distribution along the radius is nonuniform, which means the battery model parameters subject to temperature are not identical radially. This paper proposed a modified electrochemical-distributed thermal coupled model (MEDTM) for improving the accuracy of SoC estimation. The distributed thermal model is employed to design a robust H-infinity temperature observer for the estimation of the radial temperature distribution of battery cell, where a radial discretized method is used for the realization of the observer design. Based on the observed temperature, a SoC observer is developed with the backstepping method. Finally, experiments and simulation are implemented. The two constant discharging experiments indicate that MEDTM is more accurate than the single particle model with surface temperature (SPMST), and it can generate reliable temperature prediction. A comparative simulation and a constant discharging experiment verify the H-infinity temperature observer can obtain a more accurate estimation of the battery cell’s temperature than the luenberger observer, and the H-infinity temperature observer has an estimation error of 0.3 K below. Then, through a constant discharging experiment and a simulation with UDDS current, the proposed SoC observer is verified to accurately estimate the SoC by comparing with the true SoC, where the estimated error of SoC under the two cases is below 1.5% and below 0.4%, respectively. Therefore, the proposed SoC observer also has good performance.

Adaptive Square-Root Unscented Kalman Filter-Based State-of-Charge Estimation for Lithium-Ion Batteries with Model Parameter Online Identification

The state-of-charge (SOC) is a fundamental indicator representing the remaining capacity of lithium-ion batteries, which plays an important role in the battery’s optimized operation. In this paper, the model-based SOC estimation strategy is studied for batteries. However, the battery’s model parameters need to be extracted through cumbersome prior experiments. To remedy such deficiency, a recursive least squares (RLS) algorithm is utilized for model parameter online identification, and an adaptive square-root unscented Kalman filter (SRUKF) is designed to estimate the battery’s SOC. As demonstrated in extensive experimental results, the designed adaptive SRUKF combined with RLS-based model identification is a promising SOC estimation approach. Compared with other commonly used Kalman filter-based methods, the proposed algorithm has higher precision in the SOC estimation.

Online joint-prediction of multi-forward-step battery SOC using LSTM neural networks and multiple linear regression for real-world electric vehicles

Abstract Prediction of state of charge (SOC) is critical to the reliability and durability of battery systems in electric vehicles. The existing techniques are mostly model-based SOC estimation using experimental data, which are inefficient for learning the unpredictable battery state under complex real-world operating conditions of electric vehicles. This paper presents a novel machine-learning-enabled method to perform real-time multi-forward-step SOC prediction for battery systems using a recurrent neural network with long short-term memories (LSTM). The training results from a yearlong dataset show that the offline LSTM-based model can perform fast and accurate multi-forward-step prediction for battery SOC. Furthermore, the model has excellent practical application effects by taking into account weather and drivers’ driving behaviors during real vehicular operating, and the stability, flexibility, and robustness of this method are verified by 10-fold cross-validation. In order to achieve dual control of prediction accuracy and prediction horizon, we proposed an LRLSTM-based joint-prediction strategy while using LSTM and multiple linear regression algorithms, through which an accuracy benchmark can be obtained, and the prediction steps of LSTM within acceptable accuracy can be flexibly controlled. The smooth implementation of multi-forward-step SOC prediction on real-word vehicles can eliminate drivers’ mileage anxiety and safeguard vehicle operation in a big way.

State-of-Charge Observer Design for Batteries With Online Model Parameter Identification: A Robust Approach

The state-of-charge (SOC) indicates a lithium-ion battery's remaining capacity, and an accurate SOC estimation plays a crucial role in the battery's operation optimization and lifetime extension. This article studies a robust model-based SOC estimation strategy for batteries. Based on a battery equivalent circuit model, a robust recursive-least-squares algorithm is utilized for the model parameters online extraction, which avoids unnecessary experiments prior to SOC estimation for parameter identification. Compared with the conventional recursive least squares, it can effectively guarantee the parameter identification performance in spite of outliers in battery measurement signals. Then, a robust observer with the estimated model parameters is designed for the battery's SOC estimation, which can suppress the disturbance caused by unknown model errors. Theoretical analysis and extensive experimental results demonstrate the effectiveness of the designed SOC observer combined with robust recursive least-squares-based model identification.

An enhanced multi-state estimation hierarchy for advanced lithium-ion battery management

As a critically important power source for modern electric vehicles, lithium-ion batteries need to operate safely, reliably, and efficiently, which entails effective battery management systems (BMSs). How to accurately estimate internal battery states constitutes a key functionality in a BMS and needs to be designed meticulously. In this paper, a novel co-estimation hierarchy for state of charge (SOC), state of health (SOH) and state of power (SOP) in lithium-ion batteries is devised and validated experimentally. Considering the underlying coupling and characteristics among these states, a multi-time-scale estimation framework is developed for accurate estimates and moderate computational cost. First, the online, model-based SOC estimation is fulfilled by modified moving horizon estimation (mMHE) for better convergence and fault tolerance. Second, the model parameters are periodically updated by virtue of the mMHE-type optimization with a relatively long horizon. Third, the ampere-hour integral and the estimated SOC are employed to realize the capacity estimation offline. Given updated states and parameters, the model-based real-time SOP estimation reliably predicts the battery peak power respecting multiple operational constraints. Finally, the effectiveness and resilience of the joint SOC/SOH/SOP estimation is demonstrated through a number of experiments. Experimental results show that the proposed co-estimation hierarchy presents remarkable benefits, compared to separate estimation solutions. The estimation errors of SOC, voltage and capacity are less than 3%, 25 mV and 3%, respectively, for both fresh and aged cells.

Parameter updating method of a simplified first principles-thermal coupling model for lithium-ion batteries

Due to the inevitable degradation for lithium-ion batteries, the accuracy of state of charge (SOC) estimation decreases along with battery aging. How to ensure the accuracy of battery SOC estimation during a battery’s lifetime at different operating conditions leaves a big challenge. This work develops a parameter updating method of a simplified first principles-thermal coupling model that has good parameter identifiability and applicability for different operating conditions to ensure the accuracy of the model-based SOC estimation. Because updating all the model parameters offline is time-consuming, this work first conducts a model parameter sensitivity analysis and determines which parameters need to be accurately updated according to their sensitivities. Offline prediction methods are then developed to update the sensitive parameters according to their degradation laws. SOC validations show that the offline prediction methods can ensure the short-term accuracy, but the accuracy will decrease gradually along with the increase of the offline prediction errors of the capacity-related parameters. To address this problem, a multi-time-scale updating method combining the offline prediction and the capacity parameter online estimation is developed. Essential validations are provided to assess the SOC estimation accuracy using different parameter updating methods.

A Novel Temperature–Hysteresis Model for Power Battery of Electric Vehicles with an Adaptive Joint Estimator on State of Charge and Power

The battery state of charge (SOC) and state of power (SOP) are two essential parameters in the battery management system. For power lithium-ion batteries, temperature variation and the hysteresis effect are two of the main negative contributions to the accuracy of model-based SOC and SOP estimation. Thereby, a reliable circuit model is established herein to accurately estimate the working state of batteries. Considering the effect that temperature and hysteresis have on the electrical system, a unique fully-coupled temperature–hysteresis model is proposed to describe the interrelationship among capacity, hysteresis voltage, and temperature comprehensively. The key parameters of the proposed model are identified by experiments operated on lithium-ion batteries under varying ambient temperatures. Then we build a multi-state joint estimator to calculate the SOC and SOP on the basis of the temperature–hysteresis model. The effectiveness of the advanced model is verified by experiments at different temperatures. Moreover, the proposed joint estimator is verified by the improved dynamic stress test. The experimental results indicate that the proposed estimator making use of the temperature–hysteresis model can estimate SOC and SOP accurately and robustly. Our results also prove invaluable in terms of the construction of a flexible battery management system for applications in the actual industrial field.