State Of Charge Estimation Algorithm Research Articles

Robust State-of-Charge Estimation for Lithium-Ion Batteries Over Full SOC Range

Safe and reliable management of rechargeable lithium-ion batteries relies on accurate state-of-charge (SOC) estimation. SOC estimation algorithms developed based on the conventional state-space model can be inaccurate when the slope of the battery SOC to open-circuit voltage (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</sub> ) profile is close to zero, where the observability matrix of the conventional battery state-space model is ill-conditioned. This ill-conditioned observability issue is usually overlooked and results in unreliable SOC estimations. This article proposes a robust state-space model using a set of carefully selected states, making the proposed model well-conditioned over the full SOC range and insesitive to the slope of the SOC-V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</sub> profile. The proposed model, therefore, solves the observability issue and improves the SOC estimation accuracy. To examine the performance of the proposed state-space model over the full SOC range, the battery is discharged using a standard electric vehicle driving profile. Experiments are further carried out in various environmental temperature conditions to validate the robustness of the proposed model. The results show that the proposed state-space model is robust against the change of the slope of the SOC-V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</sub> profile and significantly improves the SOC estimation accuracy, rendering more than 30% improvement in various temperature conditions.

Optimal SoC Balancing Control for Lithium-Ion Battery Cells Connected in Series

The optimal state of charge (SoC) balancing control for series-connected lithium-ion battery cells is presented in this paper. A modified SoC balancing circuit for two adjacent cells, based on the principle of a bidirectional Cuk converter, is proposed. The optimal SoC balancing problem is established to minimize the SoC differences of cells and the energy loss subject to constraints of the normal SoC operating range, the balancing current, and current of cells. This optimization problem is solved using the sequential quadratic programming algorithm to determine the optimal duties of PWM signals applied to the SoC balancing circuits. An algorithm for the selection of the initial points for the optimal problem-solving process is proposed. It is applied in cases where the cost function has no decreasing part. Experimental tests are conducted for seven series-connected Samsung cells. The optimal SoC balancing control and SoC estimation algorithms are coded in MATLAB and embedded in LabVIEW to control the SoC balancing in real time. The test results show that the differences between the SoCs of cells converges to the desired range using the proposed optimal SoC balancing control strategy.

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.

State of charge prediction framework for lithium-ion batteries incorporating long short-term memory network and transfer learning

This study investigates accurate state of charge estimation algorithms for lithium-ion batteries based on the long short-term memory recurrent neural network and transfer learning. The long short-term memory network with the five typical layer topology is firstly constructed to learn the dependency of state of charge on measured variables. The transfer learning algorithm with fine-tuning strategy is then exploited to regulate the parameters of fully connected layer and share the knowledge of other layers. By this manner, the information from the source data can be applied to predict state of charge of other batteries with less training data. Additionally, a rolling learning method is developed to update the model parameters when the battery capacity is degraded. The precision and robustness of the proposed framework are comprehensively validated through comparative analysis of multitudinous sets of hyperparameters and methods. The experimental results manifest that the developed framework highlights precise estimation capability of state of charge at different aging states and time-varying temperature conditions. In addition, the proposed algorithm is verified feasible when transferred to different batteries based on only 30% training data.

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.

Research on Battery SOC Estimation Algorithm for Energy Storage Power Station

This paper takes the high-power lithium battery as the research object. The battery capacity is 40Ah. The state of charge (SOC) of lithium cannot be measured directly. We establish an equivalent circuit model of the battery and use Matlab/Simulink to simulate the equivalent circuit model of the battery. The simulation results and analysis show that the designed control strategy can accurately estimate the SOC of the battery and provide a theoretical basis for the designed algorithm in the practical application of energy storage power stations.

SOC Estimation of Li-ION Battery Based on Improved EKF Algorithm

The state of charge (SOC) is one of the important performance indicators of battery, which provides an important basis for the management and control of Battery Management System (BMS). In view of the characteristics of lithium iron phosphate battery, considering the model accuracy and calculation amount, the equivalent circuit model of improved PNGV was selected. Based on that, an improved Extended Kalman Filter (EKF) algorithm was adopted to estimate the state of charge (SOC) of Li-ion battery, which covariance matrix was modified by the Levenberg-Marquardt method. At the end of this paper, the SOC estimation algorithm was verified by MATLAB simulations. The results show that compared with the standard EKF, the improved EKF has higher estimation accuracy and anti-interference ability, and has better convergence in the estimation process.

State of Charge Estimation for Lithium-Ion Battery via MILS Algorithm Based on Ensemble Kalman Filter

Accurate state of charge (SOC) is great significant for lithium-ion battery to maximize its performance and prevent it from overcharging or overdischarging. This paper presents an ensemble Kalman filter- (EnKF-) based SOC estimation algorithm for lithium-ion battery. Firstly, the lithium-ion battery is modeled by the first-order RC equivalent circuit, and the multi-innovation least square (MILS) algorithm is used to perform online parameter identification of the model parameters. Then, the ensemble Kalman filter (EnKF) is introduced to estimate the state of charge. Finally, two typical experiments including constant current discharge experiment and cycling dynamic stress test are applied to evaluate the performance of the joint algorithm of MILS and EnKF. The experimental results show that the joint algorithm-based ensemble Kalman filter can achieve fast tracking and higher estimation accuracy for lithium-ion battery SOC.

Estimating State of Charge for xEV Batteries Using 1D Convolutional Neural Networks and Transfer Learning

In this paper we propose a one-dimensional convolutional neural network (CNN)-based state of charge estimation algorithm for electric vehicles. The CNN is trained using two publicly available battery datasets. The influence of different types of noises on the estimation capabilities of the CNN model has been studied. Moreover, a transfer learning mechanism is proposed in order to make the developed algorithm generalize better and estimate with an acceptable accuracy when a battery with different chemical characteristics than the one used for training the model, is used. It has been observed that using transfer learning, the model can learn sufficiently well with significantly less amount of battery data. The proposed method fares well in terms of estimation accuracy, learning speed and generalization capability.

Comparative study of state of charge estimation algorithms for Lithium-Ion Battery

Batteries are known to have found full applications in industries ranging from small electronic devices, mobile phones to complex systems such as electric vehicles and energy storage systems. The last one is characterized by the presence of large batteries with more than hundreds or thousands of batteries, so the process of estimation of their parameters becomes even more critical, demanding and complex. The evaluation of the state of batteries should be understood as finding the exact value of the following values: state of charge, capacity and internal resistance. The last two parameters are used to assess the health of batteries, to find available power and amount of energy respectively. Estimation the state of charge remains one of the most difficult tasks in the study of battery conditions. It is also one of the most important parameters that affect the correct operation of the battery, namely reliability, safety, performance. The main task of this paper is to present methods for reliable testing and evaluation of lithium batteries under different scenarios and conditions.

Vanadium Redox Flow Battery State of Charge Estimation Using a Concentration Model and a Sliding Mode Observer

Vanadium redox flow batteries are very promising technologies for large-scale, inter-seasonal energy storage. Tuning models from experimental data and estimating the state of charge is an important challenge for this type of devices. This work proposes a non-linear lumped parameter concentration model to describe the state of charge that differentiates the species concentrations in the different system components and allows to compute the effect of the most relevant over-potentials. Additionally, a scheme, based on the particle swarm global optimization methodology, to tune the model taking into account real experiments is proposed and validated. Finally, a novel state of charge estimation algorithm is proposed and validated. This algorithm uses a simplified version of previous models and a sliding mode control feedback law. All developments are analytically formulated and formally validated. Additionally, they have been experimentally validated in a home-made single vanadium redox flow battery cell. Proposed methods offer a constructive methodology to improve previous results in this field.

Noise Adaptive Moving Horizon Estimation for State-of-Charge Estimation of Li-Ion Battery

In this paper, a novel noise adaptive moving horizon estimation (NAMHE) method is proposed to improve the accuracy of state of charge(SOC) estimation of Li-ion batteries under the unknown noise conditions. Specifically, based on the maximum likelihood principle, the unknown statistical characteristics of the noises can be estimated to modify the recurrence expression of the NAMHE. Then, the SOC estimation algorithm is designed by combining the equivalent circuit model and the proposed NAMHE. Furthermore, the convergence of the estimation error expectation is obtained for the NAMHE algorithm. Finally, the simulation results clarify that the SOC estimation error under the different unknown noise conditions can be effectively reduced by the proposed method, compared with the traditional MHE method.

State of charge estimation of a Li‐ion battery based on extended Kalman filtering and sensor bias

The growing usage of electric vehicles (EVs) has led to significant advancements in batteries' technology. State of charge (SOC) estimation is an essential function of the battery management system—the heart of EVs and Kalman filtering is a standard SOC estimation method. Because of the non-uniformities in tuning and testing scenarios, it is challenging to quantify SOC estimation algorithms' performance. A SOC estimation algorithm is developed in this work, extended Kalman filter (EKF), and tested for variable scenarios like adding sensor noise and bias to terminal voltage and current and varying state and parameter initializations. Also, a dual EKF is implemented to estimate the sensor voltage and current bias and compared it against the state EKF to estimate SOC. Finally, a comparative study has been introduced to decide which algorithm represents the most accurate estimation for the battery parameters, and it was found that the dual EKF gave the best results.

State of charge estimation of lithium-ion battery based on double deep Q network and extended Kalman filter

The state of charge (SOC), as an important parameter of the lithium-ion battery management system (BMS), is an important factor affecting the current battery detection and safety issues. Due to the non-linear characteristics of the lithium-ion battery charging and discharging process, it is difficult to model the BMS and estimate the SOC accurately. This paper takes lithium-ion battery as the research object, designs the Markov decision process (MDP) model of lithium-ion battery energy storage prediction, establishes the second-order RC equivalent circuit model (ECM) and extended Kalman filter (EKF), and proposes a method based on double deep Q network (double DQN) to optimize the EKF parameters SOC estimation method to solve the problem of dimensionality disaster and value function overestimation generated in deep reinforcement learning (DRL). Through the effective verification of the lithium-ion battery SOC estimation algorithm, the simulation results show that compared with the traditional deep Q network (DQN) algorithm, double DQN has better convergence, adaptive ability and better estimation accuracy. It can provide new ideas for the accurate estimation of SOC.

Stage of Charge Estimation of Lithium-Ion Battery Packs Based on Improved Cubature Kalman Filter With Long Short-Term Memory Model

Accurate estimation of the state of charge (SOC) of lithium-ion battery packs remains challenging due to inconsistencies among battery cells. To achieve precise SOC estimation of battery packs, first, a long short-term memory (LSTM) recurrent neural network (RNN)-based model is constructed to characterize the battery electrical performance, and a rolling learning method is proposed to update the model parameters for improving the model accuracy. Then, an improved square root-cubature Kalman filter (SRCKF) is designed together with the multi-innovation technique to estimate the battery cell's SOC. Next, to cope with inconsistencies among battery cells, the SOC estimation values from the maximum and minimum cells are combined with a smoothing method to estimate the pack SOC. The robustness and accuracy of the proposed battery model and the cell SOC estimation method are verified by exerting the experimental validation under time-varying temperature conditions. Finally, real operation data are collected from an electric-scooter (ES) monitoring platform to further validate the generalization of the designed pack SOC estimation algorithm. The experimental results manifest that the SOC estimation error can be limited to 2% after convergence.

State of Charge Estimation for Li-Ion Batteries Based on an Unscented H-Infinity Filter

The state of charge (SOC) of lithium-ion batteries reflects their remaining capacity. Accurate estimation of SOC helps battery safety and is beneficial to the efficient management of batteries. The charging and discharging processes of lithium-Ion batteries are very complicated, and it is difficult to obtain accurate SOC estimation results. Therefore, it is important to study improved algorithms for SOC estimation for this nonlinear non-Gaussian battery system. In this paper, we propose an unscented H-infinity filter (UHF) based SOC estimation method, which combines the advantages of both the unscented Kalman filter (UKF) and the H-infinity filter (HF). The UKF propagates the sigma points through the nonlinear system and does not need the first-order linear approximation of the system equation, while the HF can suppress the non-Gaussian noise in the system to the greatest extent. The proposed UHF based SOC estimation algorithm is verified and evaluated in the battery management system, and further optimized in practical problems. Experimental results show that the proposed UHF based algorithm can perform accurate SOC estimation for lithium-ion batteries, and is superior to the UKF based SOC estimation.

Comparison of robustness of different state of charge estimation algorithms

Whether an algorithm of state of charge (SOC) estimation being able to use successfully in a real usage or not is highly determined by its robustness, because various errors including sensors’ errors, initial data errors, model parameters errors and so on disturb the calculation, and thus make the accuracy of estimation decrease significantly and even a wrong SOC be given out. However, systemic analysis of robustness of the algorithms that have been comprehensive studied or even been used in real applications still remains unsolved until now. In this study, various scenarios in which the random error such as current sensor bias, voltage sensor bias, and initial parameter identification errors exists are tested by using an ampere hour integration (Ah), the extended Kalman Filter (EKF) and a dual extended Kalman filter (DEKF) algorithm. Results show the robustness of three algorithms in the scenarios give different deviations. In case of the disturbance of the random error, the SOC can be effectively estimated by using the DEKF algorithm, since the maximum error of the SOC estimation from the algorithm is less than 3%, which is better than the results by using the EKF and the Ah integration.

The multi-innovation extended Kalman filter algorithm for battery SOC estimation

For a lithium battery, a second-order equivalent circuit model is adopted by studying the battery characteristic, and a state space equation with state of charge (SOC) being one state is constructed. To promote the SOC estimation precision of the extended Kalman filter (EKF) method for a lithium battery, this paper explores a multi-innovation extended Kalman filter (MI-EKF) algorithm to estimate the battery SOC by expanding a single innovation at current instant to multi-innovations containing information from current and previous instants. The aim is to increase the amount of information, and to get the more accurate estimated SOC. In addition, based on the battery difference equation, a stochastic gradient algorithm with a forgetting factor (FFSG) is used to identify the battery parameters. Finally, a lithium battery test bench is set up to sample charge-discharge data and to implement MATLAB simulation experiment; the experiment results confirm that the MI-EKF algorithm can accurately and effectively estimate the battery SOC.

Combined internal resistance and state-of-charge estimation of lithium-ion battery based on extended state observer

Lithium-ion battery is considered as one of the most successful energy storage methods which enables the sustainability of the renewable energy systems subject to high intermittency. To avoid the permanent damage and the potential explosion, the battery state-of-charge (SOC) serves as a characteristic operational parameter that should be maintained within a safe range. However, accurate SOC estimation is challenging in the presence of uncertainties, particularly due to the problems of unknown initial SOC value and the uncertain internal resistance. To address this uncertainties, this paper critically reviews the state-of-the-art of the current SOC researches and takes actions to propose a joint SOC and internal resistance estimation algorithm in a real-time data-driven manner. Both static and dynamic experiments are carried out to identify an equivalent circuit model (ECM) of the battery dynamics. The semi-empirical model's parameters are optimized using the experimental data. Sensitivity analysis is then carried out to reveal that the internal resistance is the dominating parameter that affects the model accuracy. A conventional model-based nonlinear state observer is developed to accommodate the initial value uncertainty. To deal with the uncertain internal resistance through this state observer, internal resistance is treated as an augmented state, which is estimated together with SOC based on extended state observer (ESO). The conclusions are drawn from the experimental results in two aspects, i) a 83% performance improvement of the proposed ESO method is achieved when compared with the conventional observer without internal resistance augmentation; ii) the dynamic variation of the internal resistance is captured by the proposed method, which is shown to increase with the service time. The proposed method is able to give a simultaneous estimation of SOC and internal resistance, depicting a promising prospect in the future commercial application.

SOC estimation algorithm of power lithium battery based on AFSA‐BP neural network

The non-linear characteristic of power lithium battery restricts the establishment of accurate battery models. To overcome this problem and estimate the battery state of charge (SOC) more accurately, the artificial fish swarm algorithm-back propagation (AFSA-BP) neural network structure was designed based on AFSA and BP neural network theory. According to the test parameters of power lithium battery, the related mathematical model was established. The flow charts of optimising BP neural network with AFSA algorithm and estimating SOC value by AFSA-BP algorithm are given. The specific implementation steps are elaborated. Using the 48 V, 50 Ah lithium iron phosphate (LiFePO4) power battery as experimental object, through the periodic charging and discharging experiments and software simulation, the correctness, validity and accuracy of the application of AFSA-BP neural network in estimating SOC value of the power lithium battery are verified.