Battery Model Parameters Research Articles

Modeling and Simulation of Lithium-ion Battery Considering the Effect of Charge-Discharge State

Establishing an accurate battery equivalent model is an important link in the development of battery management system (BMS). The second-order RC equivalent circuit model can accurately describe the dynamic characteristics of the battery. Considering the influence of state of charge (SOC) and battery charging and discharging state on the model parameters, the battery model parameters in charging state and discharging state are identified separately through battery performance test experiments. The equivalent circuit model of lithium ion battery with variable parameters is established by Simscape language, and simulation analysis is carried out. The results show that, considering the influence of battery charge and discharge state, the error of the model is small and the accuracy of the model is improved.

A Novel Adaptive Particle Swarm Optimization Algorithm Based High Precision Parameter Identification and State Estimation of Lithium-Ion Battery

Lithium-ion batteries are widely used in new energy vehicles, energy storage systems, aerospace and other fields because of their high energy density, long cycle life and high-cost performance. Accurate equivalent modeling, adaptive internal state characterization and accurate state of charge estimation are the cornerstones of expanding the application market of lithium-ion batteries. According to the highly nonlinear operating characteristics of lithium-ion batteries, the Thevenin equivalent model is used to characterize the operating characteristics of lithium-ion batteries, particle swarm optimization algorithm is used to process the measured data, and adaptive optimization strategy is added to improve the global search ability of particles, and the parameters of the model are identified innovatively. Combined with extended Kalman algorithm and Sage-Husa filtering algorithm, the state-of-charge estimation model of lithium ion battery is constructed. Aiming at the influence of fixed and inaccurate noise initial value in traditional Kalman filtering algorithm on SOC estimation results, Sage-Husa algorithm is used to adaptively correct system noise. The experimental results under HPPC condition show that the maximum error of the model is less than 1.5%. Simulation results of SOC estimation algorithm under two different operating conditions show that the maximum estimation error of adaptive extended Kalman algorithm is less than 0.05, which realizes high-precision lithium battery model parameter identification and high-precision state-of-charge estimation.

Online estimation of battery model parameters and state of health in electric and hybrid aircraft application

The accuracy of state of health (SOH) estimation function in battery management systems is an essential factor for ensuring the safety and reliability of battery systems in electric aircraft. Most common SOH estimation approaches are model-based and work with constant model parameters. However, the model parameters vary by the change in operating temperature and state of charge (SOC). The variation of model parameters has adverse impact on the accuracy of battery state's estimation if they are not updated. In this paper, an accurate online parameter estimation method is proposed for lithium-ion batteries (LIBs) to increase the accuracy of the battery model. A more accurate model for the battery leads to a more accurate SOC and SOH estimation. An adaptive sliding observer is developed to estimate the SOC and capacity based on the proposed parameter estimator. An adaptive SOH estimation scheme is proposed to mitigate the temperature variation effect on the accuracy of the SOH estimation. The experimental results verify the effectiveness of the proposed parameter estimator along with the adaptive sliding observer on achieving accurate estimation of SOC and capacity. The proposed adaptive SOH shows good agreement with experiments by less than 1.3% estimation error at different operating temperature conditions.

Joint State-of-Charge and State-of-Available-Power Estimation Based on the Online Parameter Identification of Lithium-Ion Battery Model

This article presents a joint state-of-charge (SOC) and state-of-available-power (SOAP) estimation method based on online battery model parameter identification. First, the SOAP of lithium-ion batteries is analyzed thoroughly, and a safe operating area border-based (SOAB-based) SOAP estimation is proposed. Second, based on the adaptive battery-state estimator (ABSE) and improved ABSE, a joint SOC and SOAB-based SOAP estimation method is proposed. The joint estimation results show that the improved ABSE achieves higher accuracy than the ABSE at different battery aging states. The open-loop accuracy evaluation results show that the improved ABSE identifies the battery model parameters more accurately, and the ABSE algorithm error source lies in its identified Rp being much higher than the actual value when the battery is charged/discharged at a high current. The ABSE does not consider the influence of load current on the equivalent circuit model parameters, so it is not suitable for SOAP estimation in theory. The improved ABSE proposed by our team can eliminate this modeling error, identify the battery model parameters, and estimate the SOC and SOAB-based SOAP more accurately. This improved ABSE is an effective algorithm for estimating the battery state when the battery is charged/discharged with a high current.

A Novel Adaptive Function—Dual Kalman Filtering Strategy for Online Battery Model Parameters and State of Charge Co-Estimation

This paper aims to improve the stability and robustness of the state-of-charge estimation algorithm for lithium-ion batteries. A new internal resistance-polarization circuit model is constructed on the basis of the Thevenin equivalent circuit to characterize the difference in internal resistance between charge and discharge. The extended Kalman filter is improved through adding an adaptive noise tracking algorithm and the Kalman gain in the unscented Kalman filter algorithm is improved by introducing a dynamic equation. In addition, for benignization of outliers of the two above-mentioned algorithms, a new dual Kalman algorithm is proposed in this paper by adding a transfer function and through weighted mutation. The model and algorithm accuracy is verified through working condition experiments. The result shows that: the errors of the three algorithms are all maintained within 0.8% during the initial period and middle stages of the discharge; the maximum error of the improved extension of Kalman algorithm is over 1.5%, that of improved unscented Kalman increases to 5%, and the error of the new dual Kalman algorithm is still within 0.4% during the latter period of the discharge. This indicates that the accuracy and robustness of the new dual Kalman algorithm is better than those of traditional algorithm.

State-of-charge estimation of lithium-ion battery pack by using an adaptive extended Kalman filter for electric vehicles

State-of-charge (SOC) estimation is an important aspect for modern battery management systems. Extended Kalman filter (EKF) has been extensively used in battery SOC estimation. However, EKF cannot obtain accurate estimation results when the model parameters have strong uncertainty or/and the accurate initial value of noise covariance matrix is unknown. To overcome these defects, the parameters of Lithium-ion battery model on the basis of the second-order resistor–capacitor (RC) equivalent model are identified, and then an improved adaptive EKF (IAEKF) of SOC estimation method for Lithium-ion battery pack is proposed for enhancing estimation accurate and robustness. In IAEKF, the statistical characteristics of measurement noise is adaptively corrected using a forgetting factor, namely, Sage–Husa EKF (SHEKF), and the error covariance matrix is adaptively corrected in accordance with the innovation, in which the calculation of the actual innovation covariance matrix adopts the variable sliding window length. Results of numerical simulation and experiment show that the proposed SOC estimation method can accurately estimate SOC under complex driven condition and has strong robustness to the uncertainty of model parameters and the initial value of the noise covariance matrix.

Learning to Calibrate Battery Models in Real-Time with Deep Reinforcement Learning

Lithium-ion (Li-I) batteries have recently become pervasive and are used in many physical assets. For the effective management of the batteries, reliable predictions of the end-of-discharge (EOD) and end-of-life (EOL) are essential. Many detailed electrochemical models have been developed for the batteries. Their parameters are calibrated before they are taken into operation and are typically not re-calibrated during operation. However, the degradation of batteries increases the reality gap between the computational models and the physical systems and leads to inaccurate predictions of EOD/EOL. The current calibration approaches are either computationally expensive (model-based calibration) or require large amounts of ground truth data for degradation parameters (supervised data-driven calibration). This is often infeasible for many practical applications. In this paper, we introduce a reinforcement learning-based framework for reliably inferring calibration parameters of battery models in real time. Most importantly, the proposed methodology does not need any labeled data samples of observations and the ground truth parameters. The experimental results demonstrate that our framework is capable of inferring the model parameters in real time with better accuracy compared to approaches based on unscented Kalman filters. Furthermore, our results show better generalizability than supervised learning approaches even though our methodology does not rely on ground truth information during training.

Parameter Identification and State-of-Charge Estimation for Lithium-Ion Batteries Using Separated Time Scales and Extended Kalman Filter

With the development of new energy vehicle technology, battery management systems used to monitor the state of the battery have been widely researched. The accuracy of the battery status assessment to a great extent depends on the accuracy of the battery model parameters. This paper proposes an improved method for parameter identification and state-of-charge (SOC) estimation for lithium-ion batteries. Using a two-order equivalent circuit model, the battery model is divided into two parts based on fast dynamics and slow dynamics. The recursive least squares method is used to identify parameters of the battery, and then the SOC and the open-circuit voltage of the model is estimated with the extended Kalman filter. The two-module voltages are calculated using estimated open circuit voltage and initial parameters, and model parameters are constantly updated during iteration. The proposed method can be used to estimate the parameters and the SOC in real time, which does not need to know the state of SOC and the value of open circuit voltage in advance. The method is tested using data from dynamic stress tests, the root means squared error of the accuracy of the prediction model is about 0.01 V, and the average SOC estimation error is 0.0139. Results indicate that the method has higher accuracy in offline parameter identification and online state estimation than traditional recursive least squares methods.

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.

배터리 임피던스 변화를 반영한 확장 칼만 필터를 기반으로 한 배터리 SOC 추정에 관한 연구

The state of charge(SOC) of battery should be accurately estimated because it is used as basic data for various functions of the battery management(BMS) as well as the remaining battery capacity. Extended Kalman Filter(EKF) based on a battery model is widely used as a real-time SOC estimation technique. However, the parameters of battery model are slightly different for each SOC section and changed by C-rate. As a result, if the battery parameters are used a fixed value, the accuracy of SOC estimation using EKF is decreased. In this paper, to improve the accuracy of the SOC estimation using EKF, the changes in battery parameters according to C-rate were analyzed for five SOC sections. Also, the accuracy of the SOC estimation according to the number of SOC sections was calculated by simulation. Experimental results show that the battery parameters reduce as C-rate increases. In addition, as the SOC decreased, the internal resistor R<SUB>i</SUB> and loss resistor R<SUB>d</SUB> increased, but the double layer capacitor C<SUB>d</SUB> decreased. Therefore, in order to increase the accuracy of SOC estimation using EKF, it is necessary to reflect the changes in battery parameters in each SOC section according to the C-rage. This was verified by simulation.

Real‐time identification of partnership for a new generation of vehicles battery model parameters based on the model reference adaptive system

Partnership for a new generation of vehicles (PNGV) model is a conventional battery equivalent circuit model (ECM). However, identifying the best parameters for this model is a challenge. In this study, the PNGV model is transformed into a directly identifiable difference equation to identify its parameters. Subsequently, the model reference adaptive system (MRAS) is used to realize the real-time identification of the model parameters. The identification accuracy of the MRAS is found to be superior to that of the recursive extended least square algorithm. For a single hybrid pulse power characterization (HPPC), the PNGV model identified by the MRAS can achieve a high-precision terminal voltage estimation. For lithium iron phosphate, lithium titanate, and nickel-metal hydride batteries, the root mean square errors are 0.024, 0.048, and 0.020 V, respectively. Besides, the real-time state of charge (SOC) estimation can be realized by the identified open-circuit voltage (OCV). The average errors of the three batteries are only −0.02, −0.01, and −0.01, respectively. Since the PNGV model has a capacity of describing the change of OCV with the current accumulation effect, the model is only suitable for simulating single HPPC or positive-negative pulses with equal amplitude and not for other current pulses. This is a major drawback of the PNGV model. The real-time PNGV model parameters identification method proposed in this study can provide a solid foundation for various state estimation of a battery. Novelty Statement Transformation of the PNGV model into a difference equation that can be directly identified. Real-time identification of the PNGV model parameters via the MRAS. The identified OCV realized the real-time SOC estimation and discussed the deficiencies of the PNGV model.

Combined State of Charge and State of Energy Estimation of Lithium-Ion Battery Using Dual Forgetting Factor-Based Adaptive Extended Kalman Filter for Electric Vehicle Applications

With the increasing demand for Lithium-ion batteries in an electric vehicle (EV), it is always crucial to develop a highly accurate and low-cost state estimation method for the battery management system (BMS). Presently, the dual extended Kalman filter (DEKF) is extensively utilized for online SOC estimation. However, the problem of battery model parameter divergence from the true value greatly affects the estimation accuracy under realistic dynamic loading conditions. In this paper, the new dual forgetting factor-based adaptive extended Kalman filter (DFFAEKF) is proposed for SOC estimation. The proposed SOC estimation method is combined with the simple SOE estimation approach to develop the combined SOC and SOE estimation method. The quantitative relationships between SOC and SOE for all the test battery cells, which are established with the experimental data collected from different constant current discharge profiles are employed for SOE estimation. To evaluate the performance of the developed combined SOC and SOE estimation method, the three different chemistries battery cells are chosen for the testing under different dynamic loading profiles such as dynamic stress test (DST) and US06 drive cycle. For all the considered test battery cells, the experimental results indicated that the combined SOC and SOE estimation method using the proposed DFFAEKF can estimate the battery states under dynamic operating conditions with root mean square error (RMSE) less than 0.85% and 0.95% respectively. The proposed method also demonstrates fast convergence to its true value under erroneous initial conditions. Additionally, the order of worst-case big O notation complexity of the proposed DFFAEKF is equivalent to DEKF. Besides, the simplicity of the proposed method also supports to reduce the computational burden of the processor used in BMSs, and therefore it is well-suited for EV applications.

Compensation Method for Estimating the State of Charge of Li-Polymer Batteries Using Multiple Long Short-Term Memory Networks Based on the Extended Kalman Filter

Many battery state of charge (SOC) estimation methods have been studied for decades; however, it is still difficult to precisely estimate SOC because it is nonlinear and affected by many factors, including the battery state and charge–discharge conditions. The extended Kalman filter (EKF) is generally used for SOC estimation, however its accuracy can decrease owing to the uncertain and inaccurate parameters of battery models and various factors with different time scales affecting the SOC. Herein, a SOC estimation method based on the EKF is proposed to obtain robust accuracy, in which the errors are compensated by a long short-term memory (LSTM) network. The proposed approach trains the errors of the EKF results, and the accurate SOC is estimated by applying calibration values corresponding to the condition of the battery and its load profiles with the help of LSTM. Furthermore, a multi-LSTM structure is implemented, and it adopts the ensemble average to guarantee estimation accuracy. SOC estimation with a root mean square error of less than 1% was found to be close to the actual SOC calculated by coulomb counting. Moreover, once the EKF model was established and the network trained, it was possible to predict the SOC online.

Estimation of state of charge of lithium battery based on parameter identification of fractional order model

Accurate estimation of state of charge of lithium battery is one of the important performance parameters for safe and reliable operation of lithium battery. A fractional order second-order Thevenin equivalent circuit model was proposed by based on the improvement of the traditional Thevenin equivalent circuit model for accurately estimating the state of charge of lithium-ion battery. In order to overcome the shortcomings of the least square method easily enter into local convergence or even unable to converge, an adaptive genetic algorithm is proposed to identify the parameters of lithium battery model, and global parameter identification is carried out to improve the convergence of the algorithm. Matlab simulation shows that the parameters of fractional order model of the second-order Thevenin equivalent circuit identified by adaptive genetic algorithm are better than those of integer order model identified by least square method. Combined with extended Kalman filter, the estimation of state of charge accuracy control is realized, with the accuracy error being within 1.61%.

A Method of State-of-Charge Estimation for EV Power Lithium-Ion Battery Using a Novel Adaptive Extended Kalman Filter

Battery management system (BMS) is one of the key subsystems of electric vehicle, and the battery state-of -charge (SOC) is a crucial input for the calculations of energy and power. Therefore, SOC estimation is a significant task for BMS. In this paper, a new method for online estimating SOC is proposed, which combines a novel adaptive extended Kalman filter (AEKF) and a parameter identification algorithm based on adaptive recursive least squares (RLS). Specifically, according to the first order R-C network equivalent circuit model, the battery model parameters are identified online using the RLS with multiple forgetting factors. Based on the identified parameters, the novel AEKF is used to accurately estimate the battery SOC. The online identification of parameter tracks the varying model. At the same time, due to the novel AEKF algorithm to dynamically adjust the system noise parameter, excellent accuracy of the SOC real-time estimation is obtained. Experiments are set to evaluate the accuracy and robustness of the proposed SOC estimation method. The simulation test results indicate that under DST and UDDS conditions, the maximum absolute errors are less than 0.015 after filtering convergence. In addition, the maximum absolute error is less than 0.02 in the simulation of DST with current and voltage measurement noise, so is in DST with current offset sensor error. The tests indicate that the proposed method can accurately estimate battery SOC and has strong robustness.

Development of a Model-Based Approach to Capture Battery Parameter Degradation in Satellites

There is an increasing number of CubeSats being launched on the Earth’s orbit. They are typically based on commercial off-the-shelf batteries that are not primarily designed for space applications. Thus, their actual degradation in this environment needs to be considered, compared to on-ground laboratory conditions. In this work, a model-based method is introduced for tracking the change in battery model parameters, including the battery capacity. The method is based on collected telemetry data and it covers specific and variable battery temperature conditions in CubeSats. However, it is shown that the method is sensitive to telemetry quality, regarding sample resolution and sample loss. Thus, the used settings could not determine battery degradation trends with high confidence. Nevertheless, steps for improvement were identified that shall increase the accuracy of the results in future work.

Multi‐phase method of estimation and adaptation of parameters of electrical battery models

Mathematical modeling of the battery lifetime is an important tool for the design of more efficient batteries, as well as for the optimization of their use. The electrical models class is among the classes of mathematical models used for this purpose, and a fundamental step to their application is the correct estimation of their parameters. This paper performs the mathematical modeling of Lithium-Ion Polymer batteries lifetime through the electrical model of Tremblay, in which a multi-phase method of estimation and adaptation of parameters is proposed, divided into three phases: discovery, learning, and inference. The multi-phase method is based on two Artificial Intelligence techniques: genetic algorithms and artificial neural networks. The proposed method is validated by the simulation and experimental studies. From the results, it is concluded that the application of the multi-phase method improves the effective accuracy of the Tremblay model, when it comes to adapt its parameters to the battery during runtime. For constant discharge currents, the average error reduction was 79%, when compared to the best set of parameters obtained by GA without the adaptation process. For variable current discharge curves, the method was able to reduce the error more than 35%. This method can be applied to other battery lifetime prediction models.

State-of-charge estimation based on model-adaptive Kalman filters

This article presents a set of algorithms for the estimation of state of charge, specifically deployed for lithium-ion batteries. These algorithms are based on appropriate battery models. These models can be developed having different levels of accuracy, also including the possibility to correctly represent the hysteresis voltage behaviour of the selected lithium cells. In addition, different identification methods of the battery model parameters may also be considered, considering tabulated parameters, calibrated in previous tests, or online parametrization tools. State of charge is then evaluated using non-linear Kalman filter techniques. Effectiveness of identification methods, also with the performance offered by Kalman filter itself, has been accurately evaluated through experimental tests. To verify the robustness of the proposed algorithms, some disturbances were introduced and evaluation was also conducted at different state of charge initial conditions and sampling times.

State of Power Prediction for Lithium-Ion Batteries in Electric Vehicles via Wavelet-Markov Load Analysis

Electric vehicle (EV) power demands come from its acceleration/braking as well as consumptions of the components. The power delivered to meet any demand is limited to the available power of the battery. This makes the battery state of available power (SoAP) a critical variable for battery management purposes. This article presents a novel approach for long-term SoAP prediction by supervising the working conditions for prediction of future load. Firstly, a battery equivalent circuit model (ECM) coupled with a thermal model is established to accurately capture the battery dynamics. The battery model is then connected to an EV model in order to interpret the working conditions to battery power demand. By supervising the historical usage conditions, a long-term load prediction mechanism is designed based on wavelet analysis and Markov models. This facilitates the separation of low and high frequency load demands and addresses future uncertainties. Finally, the SoAP prediction is put forward along with a sensitivity analysis with respect to battery model and load prediction mechanism parameters. It is demonstrated that compared to the existing approaches for load and SoAP prediction, the developed method is more practical and accurate. Co-simulations via MATLAB and AMESim as well as experiments on a set of commercially available Lithium-ion (Li-ion) cylindrical cells under real-world drive cycles prove the given concept and validate the performance of the method.

State of Charge Estimation for Lithium-Ion Power Battery Based on H-Infinity Filter Algorithm

To accurately estimate the state of charge (SOC) of lithium-ion power batteries in the event of errors in the battery model or unknown external noise, an SOC estimation method based on the H-infinity filter (HIF) algorithm is proposed in this paper. Firstly, a fractional-order battery model based on a dual polarization equivalent circuit model is established. Then, the parameters of the fractional-order battery model are identified by the hybrid particle swarm optimization (HPSO) algorithm, based on a genetic crossover factor. Finally, the accuracy of the SOC estimation results of the lithium-ion batteries, using the HIF algorithm and extended Kalman filter (EKF) algorithm, are verified and compared under three conditions: uncertain measurement accuracy, uncertain SOC initial value, and uncertain application conditions. The simulation results show that the SOC estimation method based on HIF can ensure that the SOC estimation error value fluctuates within ±0.02 in any case, and is slightly affected by environmental and other factors. It provides a way to improve the accuracy of SOC estimation in a battery management system.