Initial State Of Charge Error Research Articles

State of charge estimation of lithium-titanate battery based on multi-model extended Kalman filter considering temperature and current rate

To tackle the issue of accurately estimating the state of charge (SOC) of lithium-titanate (Li-Ti) batteries in complex vehicle applications, a multi-model extended Kalman filter (MM-EKF) algorithm considering the effects of temperature and current rate is proposed. Based on the operational characteristics of Li-Ti batteries in the context of electric vehicle applications, second-order RC equivalent circuit models (ECMs) are established to account for the temperature and current rate influences. Model parameters are identified using an adaptive recursive least squares method with a forgetting factor based on experimental data. Subsequently, a SOC estimation method based on the MM-EKF algorithm for Li-Ti batteries is proposed and its effectiveness is validated under different ambient temperatures. Experimental results demonstrate that the MM-EKF algorithm, which considers the effects of temperature and current rate, can accurately estimate the SOC of Li-Ti batteries. The maximum estimation error is within 5 % at different ambient temperatures, and the algorithm can quickly eliminate initial SOC errors. Consequently, it fulfills the requirements for SOC estimation of hybrid tracked vehicles in intricate operating conditions.

High-Precision and Robust SOC Estimation of LiFePO4 Blade Batteries Based on the BPNN-EKF Algorithm

The lithium iron phosphate (LiFePO4) blade battery is a long, rectangular-shaped cell that can be directly integrated into battery pack systems. It enhances volumetric power density, significantly reduces costs, and is widely utilized in electric vehicles. However, the flat open circuit voltage and significant polarization differences under wide operational temperatures are challenging for accurate voltage modeling of battery management systems (BMSs). In particular, inaccurate state of charge (SOC) estimation may cause overcharging and over-discharging risks. To accurately perceive the SOC of LiFePO4 blade batteries, a SOC estimation method based on the backpropagation neural network-extended Kalman filter (BPNN-EKF) algorithm is proposed. BPNN is a neural network model that utilizes the backpropagation algorithm to update model parameters, while EKF is an optimal estimation algorithm. Firstly, dynamic working condition tests, including the New European Driving Cycle (NEDC) and high-speed working (HSW) condition tests, are conducted under a wide temperature range (−25–43 °C). HSW conditions refer to a simulated operating condition that mimics the driving of an electric vehicle on a highway. The minimum voltage of the battery system is used as the output for training the BPNN model. We derive the Kalman gain by combining the BPNN output voltage. Additionally, the EKF algorithm is employed to correct the SOC value using voltage error information. Concerning long SOC calculation intervals, capacity errors, initial SOC errors, and current and voltage sampling errors, the maximum SOC estimation RMSE is 3.98% at −20 °C NEDC, 3.62% at 10 °C NEDC, and 1.68% at 35 °C HSW. The proposed algorithm can be applied to different temperatures and operations, demonstrating high robustness. This BPNN-EKF algorithm has the potential to be embedded in electric vehicle BMS systems for practical applications.

Novel method for modelling and adaptive estimation for SOC and SOH of lithium-ion batteries

Equivalent circuit models of lithium-ion batteries are the foundation of accurately estimating state of charge (SOC) and state of health (SOH). To further describe the performance of the batteries between working and idling states, we present for the first time the analysis of an improved fractional-order model (IFOM). Moreover, an endogenous immune algorithm (EIA) is proposed to identify the parameters of the model. Meanwhile, considering the aging effect, an adaptive dual square root Kalman filtering (ADSRCKF) with the dormancy zone is proposed to achieve the estimation. The first filter in ADSRCKF estimates SOC and SOH in which the SOH is characterised by the ohmic resistance. The second filter adaptively updates the drifted model parameters according to the dormancy zone. Finally, the proposed method is evaluated with the random walk charging and discharging test. The experimental results illustrate that the adaptively updated parameters can better match the battery status in real time, and the proposed ADSRCKF can achieve high accuracy with strong robustness. For the initial SOC error, the root mean square error (RMSE) of SOC is less than 0.3%, and the RMSE is approximately 1% even when the initial capacity is also deviated.

State of charge estimation of lithium-ion phosphate battery based on weighted multi-innovation cubature Kalman filter

State of charge (SoC) is one of the most important parameters of battery manage system (BMS). To obtain a better result of SoC estimation, an accurate battery model and effective SoC estimation algorithm are indispensable. In this work, a Thevenin model is established and linear Kalman filter (LKF) is used for online parameters identification. Results show that convergence of parameters identification of LKF is better than that of the recursive least squares (RLS) and recursive least squares with forgetting factor (FFRLS). In addition, the equilibrium potential equation (EPE) is used to fit the relationship between open circuit voltage (OCV) and SoC instead of 9th order polynomial. Then, by the weighted calculation of the innovation vector based on error distribution and time distribution, the weighted multi-innovation cubature Kalman filter (WMICKF) is proposed for the SoC estimation. The experimental data are obtained based on a prismatic LiFePO4 battery, which is tested under urban dynamometer driving schedule (UDDS) test and new European driving cycle (NEDC) test at room temperature. The results show that the WMICKF outperforms the classical cubature Kalman filter (CKF) and the multi-innovation CKF (MICKF). The SoC estimation error of WMICKF can be limited within 1% (0.91%), which is better than 1.30% of CKF and 2.71% of MICKF. In addition, the mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R-square) are calculated for comprehensive assessment of the proposed method. Furthermore, the robustness of WMICKF is verified under different initial SoC error and different types of noise disturbance. Results show that under these uncertain factors, the proposed WMICKF is still reliable for accurate SoC estimation.

Online SoC Estimation of Lithium-Ion Batteries Using a New Sigma Points Kalman Filter

The accurate state of charge (SoC) online estimation for lithium-ion batteries is a primary concern for predicting the remaining range in electric vehicles. The Sigma points Kalman Filter is an emerging SoC filtering technology. Firstly, the charge and discharge tests of the battery were carried out using the interval static method to obtain the accurate calibration of the SoC-OCV (open circuit voltage) relationship curve. Secondly, the recursive least squares method (RLS) was combined with the dynamic stress test (DST) to identify the parameters of the second-order equivalent circuit model (ECM) and establish a non-linear state-space model of the lithium-ion battery. Thirdly, based on proportional correction sampling and symmetric sampling Sigma points, an SoC estimation method combining unscented transformation and Stirling interpolation center difference was designed. Finally, a semi-physical simulation platform was built. The Federal Urban Driving Schedule and US06 Highway Driving Schedule operating conditions were used to verify the effectiveness of the proposed estimation method in the presence of initial SoC errors and compare with the EKF (extended Kalman filter), UKF (unscented Kalman filter) and CDKF (central difference Kalman filter) algorithms. The results showed that the new algorithm could ensure an SoC error within 2% under the two working conditions and quickly converge to the reference value when the initial SoC value was inaccurate, effectively improving the initial error correction ability.

Parameter and State of Charge Estimation Simultaneously for Lithium‐Ion Battery Based on Improved Open Circuit Voltage Estimation Method

Herein, the improved open‐circuit voltage (OCV) estimation method is developed and applied to estimate the model parameters and state of charge (SOC) for lithium‐ion batteries simultaneously. First, the OCV and SOC mapping relationship with temperature dependence is explored with the help of the low‐current OCV test and the improved OCV estimation method is proposed for all test temperatures. Afterward, the dual adaptive extended Kalman filter (DAEKF) based on the residual sequence is utilized to identify the model parameters and estimate the SOC simultaneously. Finally, the proposed approach is verified with 50% initial SOC error and compared with the residual sequence‐based DEKF method at different temperatures under the Federal Urban Driving Schedule (FUDS) test. The results of this study indicate that the proposed DAEKF based on the proposed improving OCV estimation method and residual sequence could achieve higher SOC estimation accuracy with good robustness at all test temperatures.

An algorithm for state of charge estimation based on a single-particle model

Compared with the equivalent circuit models or other empirical models, a physics-based model has advantages of accurate and elaborate, and thus becomes a potential candidate used to estimate states of Li-ion batteries in a battery management systems (BMS). The traditional pseudo-two-dimensional (P2D) model couples a large number of nonlinear partial differential equations, leading to the model too complicated to be employed in actual application. The simplified single-particle (SP) model has a trend for the real usage, however, its accuracy needs to be improved, since it meets the demand only under the condition of a low charge/discharge rate. To overcome the drawbacks of the SP model, the extended single-particle model (ESP) with higher accuracy is proposed in this study. We also propose a new state of charge (SOC) closed-loop estimation algorithm based on the combination of ESP model and the ampere-hour integration. Results show that the ESP model can effectively simulate the performance of the battery, and the closed-loop SOC estimation algorithm can correct the initial SOC error without increasing the computational complexity. The mean error of the closed-loop SOC estimation based on ESP is reduced by about 95% and 92.5% than ampere-hour integration under 1 C discharge and FUDS discharge, respectively.

A Novel Method for State of Charge Estimation of Lithiumion Batteries using Embedded Cubature Kalman Filter

The accurate estimation of state of charge (SOC) of Lithium-ion battery is one of the most crucial issues for battery management system (BMS). This paper proposes a novel method for SOC estimation using the embedded cubature Kalman filter (ECKF). ECKF computes the cubature points with a weight depends on an optional parameter, which differs from the standard cubature Kalman filter (CKF). An online model identification method for a second-order RC networks equivalent circuit model using the forgetting factor recursive least squares (FRLS) algorithm has been presented. The Dynamic cycles are used to assess the superiority in improving the accuracy and stability of proposed method compared with the widely used algorithms. Experimental results show that, with 20% initial SOC error, the maximum estimation error is within 1%, which indicates that the proposed ECKF method has higher estimation accuracy and robustness for SOC estimation.

A State of Charge Estimation Method for Lithium-Ion Battery Using PID Compensator-Based Adaptive Extended Kalman Filter

With the widespread application of electric vehicles, the study of the power lithium-ion battery (LIB) has broad prospects and great academic significance. The state of charge (SOC) is one of the key parts in battery management system (BMS), which is used to provide guarantee for the safe and efficient operation of LIB. To obtain the reliable SOC estimation result under the influence of simple model and measurement noise, a novel estimation method with adaptive feedback compensator is presented in this paper. The simplified dynamic external electrical characteristic of LIB is represented by the one-order Thevenin equivalent circuit model (ECM) and then the ECM parameters are identified by the forgetting factor recursive least squares method (FFRLS). Fully taking into account the feedback effect of terminal voltage innovation, the combination of adaptive extended Kalman filter (AEKF) and innovation vector-based proportional-integral-derivative (PID) feedback is proposed to estimate the LIB SOC. The common single proportional feedback of Kalman filter (KF) is replaced by the innovation vector-based PID feedback, which means that the multiple prior terminal voltage innovation is used in the measurement correction step of KF. The results reveal that the AEKF with PID feedback compensation strategy can improve the SOC estimation performance compared with the common AEKF, and it reveals good robust capability and rapid convergence speed for initial SOC errors. The maximum absolute error and average absolute error for SOC estimation are close to 4% and 2.6%, respectively.

Online Parameter Identification and State of Charge Estimation of Battery Based on Multitimescale Adaptive Double Kalman Filter Algorithm

An accurate state of charge (SOC) can provide effective judgment for the BMS, which is conducive for prolonging battery life and protecting the working state of the entire battery pack. In this study, the first-order RC battery model is used as the research object and two parameter identification methods based on the least square method (RLS) are analyzed and discussed in detail. The simulation results show that the model parameters identified under the Federal Urban Driving Schedule (HPPC) condition are not suitable for the Federal Urban Driving Schedule (FUDS) condition. The parameters of the model are not universal through the HPPC condition. A multitimescale prediction model is also proposed to estimate the SOC of the battery. That is, the extended Kalman filter (EKF) is adopted to update the model parameters and the adaptive unscented Kalman filter (AUKF) is used to predict the battery SOC. The experimental results at different temperatures show that the EKF-AUKF method is superior to other methods. The algorithm is simulated and verified under different initial SOC errors. In the whole FUDS operating condition, the RSME of the SOC is within 1%, and that of the voltage is within 0.01 V. It indicates that the proposed algorithm can obtain accurate estimation results and has strong robustness. Moreover, the simulation results after adding noise errors to the current and voltage values reveal that the algorithm can eliminate the sensor accuracy effect to a certain extent.

Comparative Study of Four Filter-based Algorithms for State-of-charge Estimation of Lithium-ion Batteries

Accurate estimation of state of charge (SOC) is greatly crucial for safely and reliably charging and discharging the lithium-ion batteries, especially for those used in electric vehicles (EVs). Currently, a lot of algorithms have been proposed to estimate the battery SOC. In this paper, we compared four filter-based algorithms, including the standard particle filter (PF), the unscented Kalman filter, the unscented Kalman-particle filter (UPF), and the extended Kalman-particle filter (EPF), in terms of the estimate accuracy and convergence rate. The federal urban driving schedule (FUDS) and the urban dynamometer driving schedule (UDDS) were applied to evaluate the performance of these estimation algorithms. Comparison results showed that compared with the UKF, the PF can improve the estimate accuracy, however, it takes much more time to correct the initial SOC error. By introducing the EKF and UKF into the particle filter, the convergence rate can be greatly improved without the decrease in estimate accuracy, and convergence rate is very close to that of the UKF.

State-of-charge estimation of lithium-ion battery using an improved neural network model and extended Kalman filter

Accurate state-of-charge (SoC) estimation is remarkably difficult due to nonlinear characteristics of batteries and complex application environment in electric vehicles (EVs), particularly low temperature and low SoC. In this paper, an improved battery model is first built using a feedforward neural network (FFNN) by introducing newly defined inputs. Based on the FFNN model and the extended Kalman filter algorithm, a FFNN-based SoC estimation method is designed, and its robustness is verified and discussed using the experimental data obtained at different temperatures. Finally, a hardware-in-loop test bench is built to further evaluate the real-time and generalization of the designed FFNN model. The results show that the SoC estimation can converge to the reference value at erroneous settings of an initial SoC error and an initial capacity error, and the SoC estimation errors can be stabilized within 2% after convergence, which applies to all the cases discussed in this paper, including low temperature and low SoC. This indicates that the FFNN-based method is an effective method to estimate SoC accurately in complex EV application environment.

An Improved Model-Based Self-Adaptive Filter for Online State-of-Charge Estimation of Li-Ion Batteries

Accurate battery modeling is essential for the state-of-charge (SOC) estimation of electric vehicles, especially when vehicles are operated in dynamic processes. Temperature is a significant factor for battery characteristics, especially for the hysteresis phenomenon. Lack of existing literatures on the consideration of temperature influence in hysteresis voltage can result in errors in SOC estimation. Therefore, this study gives an insight to the equivalent circuit modeling, considering the hysteresis and temperature effects. A modified one-state hysteresis equivalent circuit model was proposed for battery modeling. The characterization of hysteresis voltage versus SOC at various temperatures was acquired by experimental tests to form a static look-up table. In addition, a strong tracking filter (STF) was applied for SOC estimation. Numerical simulations and experimental tests were performed in commercial 18650 type Li(Ni1/3Co1/3Mn1/3)O2 battery. The results were systematically compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF). The results of comparison showed the following: (1) the modified model has more voltage tracking capability than the original model; and (2) the modified model with STF algorithm has better accuracy, robustness against initial SOC error, voltage measurement drift, and convergence behavior than EKF and UKF.

Error Analysis of the Model-Based State-of-Charge Observer for Lithium-Ion Batteries

Model-based observers are widely applied in state-of-charge (SOC) estimation. The existing model-based observers can achieve high precision in theory, but the estimation precision is influenced by many factors in practical application. The impact of the possible error sources on the SOC estimation needs to be clarified in order to enhance the practical estimation accuracy. In this paper, the effect of five error sources in the model-based SOC observer is analyzed, including the initial error, the capacity error, the current measurement error, the voltage measurement error, and the model prediction error. Both theoretical derivation and simulation analysis are implemented. The results show that the initial SOC error converges to zero during the iteration, while the errors of the capacity, current, voltage, and model cause the SOC estimation error in different extents. Quantitative comparisons of these different error sources are carried out in order to determine the critical factors of the SOC estimation. The SOC estimation accuracy is mainly limited by the model precision under the current hardware and software conditions of the battery management system, indicating a possible improving direction of the SOC estimation.

An Online State of Charge Estimation Algorithm for Lithium-Ion Batteries Using an Improved Adaptive Cubature Kalman Filter

An accurate state of charge (SOC) estimation of the on-board lithium-ion battery is of paramount importance for the efficient and reliable operation of electric vehicles (EVs). Aiming to improve the accuracy and reliability of battery SOC estimation, an improved adaptive Cubature Kalman filter (ACKF) is proposed in this paper. The battery model parameters are online identified with the forgetting factor recursive least squares (FRLS) algorithm so that the accuracy of SOC estimation can be further improved. The proposed method is evaluated by two driving cycles, i.e., the New European Driving Cycle (NEDC) and the Federal Urban Driving Schedule (FUDS), and compared with the existing unscented Kalman filter (UKF) and standard CKF algorithms to verify its superiority. The experimental results reveal that comparing with the UKF and standard CKF, the improved ACKF algorithm has a faster convergence rate to different initial SOC errors with higher estimation accuracy. The root mean square error of SOC estimation without initial SOC error is less than 0.5% under both the NEDC and FUDS cycles.

A multi-model probability SOC fusion estimation approach using an improved adaptive unscented Kalman filter technique

Abstract Battery model is crucial for the accurate estimation of the state of charge (SOC) in a battery management system of electric vehicles. However, differences exist within optimal battery models corresponding to different types of batteries. Even for the same type of battery, the corresponding optimal battery model may vary with the change of the battery status. To solve the problem, this paper proposes a multi-model probability fusion estimation (MMPFE) method to realize an accurate description of battery characteristics and a precise SOC estimation. An improved adaptive unscented Kalman filter (AUKF) approach is developed for measurement noise variance online update based on the idea of orthogonality between residual and innovation during the SOC estimation. Finally, the proposed MMPFE method was verified by experiments using LiFeO4 and LiMnO2 batteries, respectively. Results indicate that when a voltage drift of +3 mV was applied on the LiFeO4 battery under UDDS condition and an initial SOC error was applied on LiMnO2 battery under FUDS condition at different temperatures, the proposed method still can estimated the precise SOC. Comparing with the results obtained by the other methods under the same conditions, the method presented in the paper shows a higher SOC estimation accuracy and better robustness.

A model-based adaptive state of charge estimator for a lithium-ion battery using an improved adaptive particle filter

Obtaining accurate parameters, state of charge (SoC) and capacity of a lithium-ion battery is crucial for a battery management system, and establishing a battery model online is complex. In addition, the errors and perturbations of the battery model dramatically increase throughout the battery lifetime, making it more challenging to model the battery online. To overcome these difficulties, this paper provides three contributions: (1) To improve the robustness of the adaptive particle filter algorithm, an error analysis method is added to the traditional adaptive particle swarm algorithm. (2) An online adaptive SoC estimator based on the improved adaptive particle filter is presented; this estimator can eliminate the estimation error due to battery degradation and initial SoC errors. (3) The effectiveness of the proposed method is verified using various initial states of lithium nickel manganese cobalt oxide (NMC) cells and lithium-ion polymer (LiPB) batteries. The experimental analysis shows that the maximum errors are less than 1% for both the voltage and SoC estimations and that the convergence time of the SoC estimation decreased to 120s.

State of charge estimation of lithium-ion batteries using an optimal adaptive gain nonlinear observer

Accurate state of charge (SOC) estimation is very crucial to guarantee the safety and reliability of lithium-ion batteries, especially for those used in electric vehicles. Since the SOC is unmeasurable and nonlinearly varies with factors (e.g., current rate, battery degeneration, ambient temperature and measurement noise), a reliable and robust algorithm for SOC estimation is expected. In this paper, an optimal adaptive gain nonlinear observer (OAGNO) for SOC estimation is proposed. The particle swarm optimization (PSO) algorithm is employed to optimize parameters of the adaptive gain nonlinear observer (AGNO). A combined error is presented as the fitness function to evaluate the search performance of the PSO algorithm. To perform the PSO-based parameter optimization of the AGNO, a combined dynamic loading profile consisting of the Federal Urban Driving Schedule, the New European Driving Cycle and the Dynamic Stress Test is developed. The proposed approach is verified by experiments performed on Panasonic NCR18650PF lithium-ion batteries and compared with different parametric AGNOs. Experimental results indicate that the proposed OAGNO is helpful to improve the accuracy of battery SOC estimation compared with the non-optimal AGNO methods. Additionally, the OAGNO approach is robust against initial SOC error, current noise and different driving cycles.

A combination Kalman filter approach for State of Charge estimation of lithium-ion battery considering model uncertainty

An accurate battery State of Charge estimation plays an important role in battery electric vehicles. This paper makes two contributions to the existing literature. (1) A recursive least squares method with fuzzy adaptive forgetting factor has been presented to update the model parameters close to the real value more quickly. (2) The statistical information of the innovation sequence obeying chi-square distribution has been introduced to identify model uncertainty, and a novel combination algorithm of strong tracking unscented Kalman filter and adaptive unscented Kalman filter has been developed to estimate SOC (State of Charge). Experimental results indicate that the novel algorithm has a good performance in estimating the battery SOC against initial SOC errors and voltage sensor drift. A comparison with the unscented Kalman filter-based algorithms and adaptive unscented Kalman filter-based algorithms shows that the proposed SOC estimation method has better accuracy, robustness and convergence behavior.

State of Charge Estimation of Lithium-Ion Batteries Using an Adaptive Cubature Kalman Filter

Accurate state of charge (SOC) estimation is of great significance for a lithium-ion battery to ensure its safe operation and to prevent it from over-charging or over-discharging. However, it is difficult to get an accurate value of SOC since it is an inner sate of a battery cell, which cannot be directly measured. This paper presents an Adaptive Cubature Kalman filter (ACKF)-based SOC estimation algorithm for lithium-ion batteries in electric vehicles. Firstly, the lithium-ion battery is modeled using the second-order resistor-capacitor (RC) equivalent circuit and parameters of the battery model are determined by the forgetting factor least-squares method. Then, the Adaptive Cubature Kalman filter for battery SOC estimation is introduced and the estimated process is presented. Finally, two typical driving cycles, including the Dynamic Stress Test (DST) and New European Driving Cycle (NEDC) are applied to evaluate the performance of the proposed method by comparing with the traditional extended Kalman filter (EKF) and cubature Kalman filter (CKF) algorithms. Experimental results show that the ACKF algorithm has better performance in terms of SOC estimation accuracy, convergence to different initial SOC errors and robustness against voltage measurement noise as compared with the traditional EKF and CKF algorithms.