Online State Of Charge Estimation Research Articles

A Hierarchical Approach for Finite-Time H-$\infty$ State-of-Charge Observer and Probabilistic Lifetime Prediction of Lithium-Ion Batteries

Accurate state-of-charge (SOC) estimation and lifetime prognosis of lithium-ion batteries are of great significance for reliable operations of energy storage systems. This paper proposes a novel two-layer hierarchical approach for online SOC estimation and remaining-useful-life (RUL) prediction based on a robust observer and Gaussian-process-regression (GPR). At the bottom layer, an equivalent-circuit model is first developed to describe battery dynamics. Second, a combination method of a recursive least square method and a finite time H- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\infty$</tex-math></inline-formula> observer is designed to estimate battery open-circuit-voltage (OCV) and SOC through stability and robustness analysis. Next, the estimated OCV and SOC are fed into the top layer to generate the incremental-capacity-analysis-based aging feature, through which a robust signature associated with battery aging is identified. The feature is further employed for RUL prediction based on GPR. The salient advantages of the proposed approach are that it can provide robust parameter estimation in a given finite-time interval, and the GPR-based RUL prediction can tackle long-term uncertainties in a principled Bayesian manner. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed SOC observer and lifetime prediction methods.

A computationally efficient adaptive online state-of-charge observer for Lithium-ion battery for electric vehicle

Due to the large number of cells installed in electric vehicle (EV), its battery management system (BMS) requires efficient state of charge (SOC) estimation algorithm. Since there is an impetus to reduce the computational burden (while retaining an acceptable accuracy), this paper proposes a simple and fast online adaptive observer for SOC estimation of Lithium-ion battery. The observer has several attractive features: first, its stability is proven by Lyapunov approach where asymptotic error convergence is guaranteed. Second, the computational requirements are low since it contains a few simple recursive equations without matrix inversion. Third, it is adaptive and achieves simultaneous online estimation of SOC and most of the battery parameters. The practical implementation using a 3 Ah battery proves the effectiveness of the proposed observer under dynamic stress test (DST). The testing with real EV profiles (supplemental federal test procedure which is known as US06 and federal urban driving schedule FUDS) is also performed to show the reliability. It is confirmed that the computation time of the proposed algorithm is reduced by approximately 2.5 times in compared to the extended Kalman filter-recursive least square (EKF-RLS) method. Despite the reduction in computation time, the errors are comparable to the latter. The low computational cost is significant when considering the need to accurately estimate the SOC of a large number of cells in a battery pack of an EV.

Deep learning enabled state-of-charge estimation of LiFePO4 batteries: A systematic validation on state-of-the-art charging protocols

LiFePO4 batteries generally face a challenge of inaccurate state of charge (SoC) estimation due to the plateaus existing in the middle range of the open circuit voltage (OCV)-SoC curve. Generally, conventional SoC estimation methods are not capable of accurately estimating the SoC in this range. In this paper, a deep neural network (DNN) is constructed to estimate the SoC in the charging process. Battery data collected from five state-of-the-art charging protocols at 10 °C, 25 °C and 40 °C are used to train the DNN. The developed DNN can be used for online SoC estimation subsequently. This estimated SoC can serve as the initial SoC of the ampere-hour counting method to calculate the SoC of the discharging process. The overall maximum error and the root mean square error of the SoC estimation over charging process are within 2.5% and 0.8%, respectively. In addition, the input depth of time from 10 s to 100 s with a 10 s interval is investigated. The maximum error is less than 5% in the case of the depth time within 100 s and the error fall to 2% when the depth of time reaches 90 s.

A comparative study of different adaptive extended/unscented Kalman filters for lithium-ion battery state-of-charge estimation

To achieve more precise and reliable lithium-ion battery state-of-charge (SOC) estimation, this paper performs a comparative study of different adaptive extended Kalman filters (AEKFs)/adaptive unscented Kalman filters (AUKFs). Firstly, three scenarios are artificially established to evaluate different AEKFs/AUKFs' estimation accuracy, sensitivity to uncertainty existing in open-circuit-voltage (OCV)–SOC relationship and robustness ability against different forms of disturbances, respectively. Meanwhile, various AEKFs/AUKFs' difficulty of parameters tuning is also evaluated according to our experience. Subsequently, eight indexes that can reflect algorithms' comprehensive estimation performance are further extracted. On this basis, a novel multi-objective analysis decision method by fusion of analytic hierarchy process and entropy weight is adopted to allocate weights for extracted indexes and further compare various AEKFs/AUKFs’ comprehensive estimation performance, whose results are shown as scores. The algorithm with highest score demonstrates that it has the optimal comprehensive estimation performance and is also recommended to be used in real application. The most remarkable contribution of this work lies in the suggestions and guidance for researchers when choosing AEKFs/AUKFs for online SOC estimation.

PSO-LSSVM-based Online SOC Estimation for Simulation Substation Battery

As the emergency power supply for a simulation substation, lead-acid batteries have a work pattern featuring non-continuous operation, which leads to capacity regeneration. However, the accurate estimation of battery state of charge (SOC), a measurement of the amount of energy available in a battery, remains a hard nut to crack because of the non-stationarity and randomness of battery capacity change. This paper has proposed a comprehensive method for lead-acid battery SOC estimation, which may aid in maintaining a reasonable charging schedule in a simulation substation and improving battery’s durability. Based on the battery work pattern, an improved Ampere-hour method is used to calculate the SOC during constant current and constant voltage (CC/CV) charging and discharging. In addition, the combined Particle Swarm Optimization (PSO) and Least Squares Support Vector Machine (LSSVM) model is used to estimate the SOC during non-CC discharging. Experimental results show that this method is workable in online SOC estimation of working batteries in a simulation substaion, with the maximum relative error standing at only 2.1% during the non-training period, indicating a high precision and wide applicability.

Real-Time SoC Estimation for Li-Ion Batteries using Kalman Filter based on SBC Raspberry-Pi

Measurement of electric charge on the battery in real-time cannot be separated from external noise and disturbances such as temperature and interference. An optimal State of Charge (SoC) estimator model is needed to make the estimation more accurate. To obtain the model, the battery was tested under room temperature conditions and at a temperature of 40oC to obtain a second-order RC model for the Li-Ion battery used. Based on the test data obtained, the data will be tested first using the Kalman Filter method to get an estimate of the State of Charge (SoC). Tests were carried out using MATLAB software. After the method was tested, the online SoC Estimator design began using the Raspberry Pi Single Board Computer (SBC). After that, the estimator will be tested first using data from offline measurements and then used in real-time (online) SoC estimation measurements. The Voc before the battery discharge test was 13.16 V and after the test, the measured Voc was 11.58 V. During the discharge the Voc was reduced by 1.58 V. While the discharge data from the battery manufacturer showed the reduced Voc during the discharge was 1.2V.

Real-Time SoC Estimation for Li-Ion Batteries using Kalman Filter based on SBC Raspberry-Pi

Measurement of electric charge on the battery in real-time cannot be separated from external noise and disturbances such as temperature and interference. An optimal State of Charge (SoC) estimator model is needed to make the estimation more accurate. To obtain the model, the battery was tested under room temperature conditions and at a temperature of 40oC to obtain a second-order RC model for the Li-Ion battery used. Based on the test data obtained, the data will be tested first using the Kalman Filter method to get an estimate of the State of Charge (SoC). Tests were carried out using MATLAB software. After the method was tested, the online SoC Estimator design began using the Raspberry Pi Single Board Computer (SBC). After that, the estimator will be tested first using data from offline measurements and then used in real-time (online) SoC estimation measurements. The Voc before the battery discharge test was 13.16 V and after the test, the measured Voc was 11.58 V. During the discharge the Voc was reduced by 1.58 V. While the discharge data from the battery manufacturer showed the reduced Voc during the discharge was 1.2V.

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.

Potential of infrared temperature measurements for the online estimation of the state-of-charge of a Li-polymer battery

The knowledge of the battery status in terms of state-of-health (SoH), state-of-charge (SoC), and state-of-power (SoP) is of great significance for the efficient usage of the available stored energy and to ensure the safety of electric vehicles. The SoC is the equivalent of the fuel tank gage as it indicates the amount of energy that can still be extracted from the battery before a recharge. Many techniques have been proposed in the literature for the estimation of the SoC based on more or less complex mathematical approaches. In general, the electric parameters of the battery were used. This work aims to trace a new path for the estimation of the SoC of a lithium polymer battery using thermal parameters instead of electric ones. Temperature measurements are already used in battery management systems with a different function than SoC evaluation. The approach presented here aims to give a more prominent role to the temperature data collected during the battery operation. This can serve as a main or secondary (cross-check) tool for the online estimation of the battery Soc.The battery temperature is measured during the discharge phase at a constant current and the following resting phase. Thermal imaging in the infrared band is applied to assess the presence of 2d inhomogeneity on the battery surface. The experimental data are coupled to an extensive theoretical analysis based on the lumped parameter model applying Newton's law of cooling in transient conditions. The first objective is the estimation of the open-circuit voltage over time, which is unknown during the operation. It is put in correlation to the SoC calculated with the Coulomb counting method. The open-circuit voltage versus SoC curve is essential for the online SoC determination. Theoretical results have been validated with the data of a multi-step test cycle performed on purpose. Finally, a new method for the online SoC estimation based on temperature measurements has been set up and validated.

Optimal Charging Profile Design for Attaining Desired State of Charge in Symmetric Electrochemical Capacitor With Efficiency Analysis

The optimal utilization of ultracapacitor (symmetric electrochemical capacitor) for vehicular applications demands continuous monitoring and maintenance of its state of charge (SOC). The online estimation of SOC plays a vital role in the effective utilization of the energy storage capacity of ultracapacitors. In addition to monitoring SOC, high reliability in vehicle operation requires a predefined SOC level, as per the dynamic load requirement. For the ultracapacitor undergoing series of charge-discharge cycles, proper regulation of the SOC in accordance with the vehicle drive profile, increases the ultracapacitor life by avoiding possible stress due to undercharging/overcharging. Achieving the desired SOC in real-time warrants a mechanism for the optimal charging of the ultracapacitor. In this regard, the present article proposes an optimal charging scheme to attain a predefined SOC from any initial value, within a given time-frame. The proposed noniterative fractional calculus-based approach allows for analytically representing the charging current as a function of the desired SOC, charging duration and ultracapacitor model parameters. The scheme has been extensively validated experimentally for its effectiveness in attaining the desired SOC. Further, the appropriateness of the derived charging profiles for different operating scenarios has also been analyzed in terms of maintaining a tradeoff between faster charging and high charging efficiency.

Online SOC Estimation Based on Simplified Electrochemical Model for Lithium-Ion Batteries Considering Current Bias

State of Charge (SOC) is essential for a smart Battery Management System (BMS). Traditional SOC estimation methods of lithium-ion batteries are usually conducted using battery equivalent circuit models (ECMs) and the impact of current sensor bias on SOC estimation is rarely considered. For this reason, this paper proposes an online SOC estimation based on a simplified electrochemical model (EM) for lithium-ion batteries considering sensor bias. In EM-based SOC estimation structure, the errors from the current sensor bias are addressed by proportional–integral observer. Then, the accuracy of the proposed EM-based SOC estimation is validated under different operating conditions. The results indicate that the proposed method has good performance and high accuracy in SOC estimation for lithium-ion batteries, which facilitates the on-board application in advanced BMS.

On-line state of charge estimation of embedded metal hydride hydrogen storage tank based on state classification

With the further deterioration of environment and the depletion of fossil fuels, the alternative energy sources are urgently needed to be discovered. Hydrogen holds great promise thanks to its unlimited resources, high energy density and the environmentally friendly nature. However, its low volume density under normal temperature and pressure becomes the main challenge for on-board storage. Owing to its high potential of safety, one of the optimal solution for the future hydrogen vehicle is storing hydrogen using metal hydride (MH) under proper temperature and pressure. This work focuses on the state of charge (SOC) estimation of the embedded MH hydrogen storage tank. High precise estimating of the remaining energy will contribute to both the evaluation of reliability and the design of control strategy. A statistical model of SOC is proposed based on the database collected form laboratory experiments and real operation vehicle test. What’s more, a joint multi-classifier is designed to recognize the current state of reaction. Under this condition, the SOC of MH hydrogen storage tank is calculated through combining the state classifier and SOC model. This proposed on-line SOC estimation procedure is validated with the real operation vehicles in both charging and discharging process. It is proved to be effective with the estimation error of 0.2% during charging and 4.29% of discharging.

A Lagrange multiplier and sigma point Kalman filter based fused methodology for online state of charge estimation of lithium-ion batteries

In this paper, a fused online approach consisting of the Lagrange multiplier technique and sigma point Kalman filter (SPKF) is proposed for the lithium-ion battery model identification and state of charge (SOC) estimation, respectively. The Lagrange multiplier technique minimized the error between the reference and estimated SOC by estimating the accurate battery parameters, whereas SPKF helps to calculate non-linear system dynamics more precisely. The effectiveness of the proposed technique is evaluated using different publicly available experimental profiles such as the Beijing dynamic stress test, dynamic stress test, and hybrid pulse power characteristics. The effect of sensor accuracy on the SOC estimation is also analyzed. The comparative analysis reveals that the proposed methodology yields better performance than recursive least squares (RLS)-SPKF and forgetting factor RLS-SPKF. The maximum noted errors for the proposed technique were 0.2%, 0.4%, and 0.9% for hybrid pulse power characteristics, dynamic stress test, and Beijing dynamic stress test, respectively. The improvement in SOC estimation accuracy shows the effectiveness, superiority, and distinctiveness of the proposed approach.

State of Charge Estimation of Composite Energy Storage Systems with Supercapacitors and Lithium Batteries

This paper studies the state of charge (SOC) estimation of supercapacitors and lithium batteries in the hybrid energy storage system of electric vehicles. According to the energy storage principle of the electric vehicle composite energy storage system, the circuit models of supercapacitors and lithium batteries were established, respectively, and the model parameters were identified online using the recursive least square (RLS) method and Kalman filtering (KF) algorithm. Then, the online estimation of SOC was completed based on the Kalman filtering algorithm and unscented Kalman filtering algorithm. Finally, the experimental platform for SOC estimation was built and Matlab was used for calculation and analysis. The experimental results showed that the SOC estimation results reached a high accuracy, and the variation range of estimation error was [−0.94%, 0.34%]. For lithium batteries, the recursive least square method is combined with the 2RC model to obtain the optimal result, and the estimation error is within the range of [−1.16%, 0.85%] in the case of comprehensive weighing accuracy and calculation amount. Moreover, the system has excellent robustness and high reliability.

Adaptive Online State of Charge Estimation of EVs Lithium-Ion Batteries with Deep Recurrent Neural Networks

The State of Charge (SOC) estimation is a significant issue for safe performance and the lifespan of Lithium-ion (Li-ion) batteries. In this paper, a Robust Adaptive Online Long Short-Term Memory (RoLSTM) method is proposed to extract SOC estimation for Li-ion Batteries in Electric Vehicles (EVs). This real-time, as its name suggests, method is based on a Recurrent Neural Network (RNN) containing Long Short-Term Memory (LSTM) units and using the Robust and Adaptive online gradient learning method (RoAdam) for optimization. In the proposed architecture, one sequential model is defined for each of the three inputs: voltage, current, and temperature of the battery. Therefore, the three networks work in parallel. With this approach, the number of LSTM units are reduced. Using this suggested method, one is not dependent on precise battery models and can avoid complicated mathematical methods. In addition, unlike the traditional recursive neural network where content is re-written at any time, the LSTM network can decide on preserving the current memory through the proposed gateways. In that case, it can easily transfer this information over long paths to receive and maintain long-term dependencies. Using real databases, the experiment results illustrate the better performance of RoLSTM applied to SOC estimation of Li-Ion batteries in comparison with a neural network modeling and unscented Kalman filter method that have been used thus far.

Variable-Order Equivalent Circuit Modeling and State of Charge Estimation of Lithium-Ion Battery Based on Electrochemical Impedance Spectroscopy

In the battery management system, it is important to accurately and efficiently estimate the state of charge (SOC) of lithium-ion batteries, which generally requires the establishment of a equivalent circuit model of the battery, whose accuracy and rationality play an important role in accurately estimating the state of lithium-ion batteries. The traditional single order equivalent circuit models do not take into account the changes of impedance spectrum under the action of multiple factors, nor do they take into account the balance of practicality and complexity of the model, resulting the low accuracy and poor practicability. In this paper, the theory of electrochemical impedance spectroscopy is used to guide and improve the equivalent circuit model. Based on the analysis of the variation of the high and intermediate frequency range of the impedance spectrum with the state of charge and temperature of the battery, a variable order equivalent model (VOEM) is proposed by Arrhenius equation and Bayesian information criterion (BIC), and the state equation and observation equation of VOEM are improved by autoregressive (AR) equations. Combined with the unscented Kalman filter (UKF), a SOC online estimation method is proposed, named VOEM-AR-UKF. The experimental results show that the proposed method has high accuracy and good adaptability.

Online State-of-Charge Estimation Based on the Gas–Liquid Dynamics Model for Li(NiMnCo)O2 Battery

Accurately estimating the online state-of-charge (SOC) of the battery is one of the crucial issues of the battery management system. In this paper, the gas–liquid dynamics (GLD) battery model with direct temperature input is selected to model Li(NiMnCo)O2 battery. The extended Kalman Filter (EKF) algorithm is elaborated to couple the offline model and online model to achieve the goal of quickly eliminating initial errors in the online SOC estimation. An implementation of the hybrid pulse power characterization test is performed to identify the offline parameters and determine the open-circuit voltage vs. SOC curve. Apart from the standard cycles including Constant Current cycle, Federal Urban Driving Schedule cycle, Urban Dynamometer Driving Schedule cycle and Dynamic Stress Test cycle, a combined cycle is constructed for experimental validation. Furthermore, the study of the effect of sampling time on estimation accuracy and the robustness analysis of the initial value are carried out. The results demonstrate that the proposed method realizes the accurate estimation of SOC with a maximum mean absolute error at 0.50% in five working conditions and shows strong robustness against the sparse sampling and input error.

An Adaptive State of Charge Estimator Design for Lithium-Ion Batteries

In this paper, a data-driven approach in conjunction with an adaptive extended Kalman filter (AEKF) is presented to estimate the state of charge (SOC) of lithium-ion battery in real-time. The Thevenin battery model is used to evaluate the effects using battery voltage and current. The advantages of the Lagrange multiplier method are utilized to model the lithium-ion battery. The Lagrange multiplier method continuously decreases the model error to adjust the Kalman gain of AEKF for accurate SOC estimation. Various current profiles such as hybrid pulse test, dynamic stress test, and Beijing dynamic stress test are used to verify the adaptability, robustness, and accuracy of the proposed approach. It is observed that the proposed approach outperforms other methodologies (recursive least square–AEKF and forgetting factor recursive least square–AEKF) due to its high accuracy (mean average error of 0.32%). Additionally, the proposed approach exhibits robustness and high convergence speed despite deliberate erroneous initialization of parameters, thus indicating its applicability in online SOC estimation applications.

Rapid Open-Circuit Voltage Measurement Method for Lithium-Ion Batteries Using One-Cycle Bipolar-Current Pulse

Accurate estimation of state-of-charge (SOC) of battery is important for battery storage systems. A lookup table between the battery open-circuit voltage (OCV) and SOC has been widely adopted for online SOC estimation. However, it is time-consuming to obtain an accurate SOC-OCV correlation since the battery requires several hours to reach an inner-equilibrium state. Some acceleration methods utilized the measured terminal voltage to predict the final OCV, but they have accumulated errors. Therefore, instead of predicting the OCV, a directly fast OCV measurement method for lithium-ion batteries based on one-cycle bipolar-current pulse, namely, a positive current pulse followed by a negative current pulse with the same duration and amplitude is proposed in this article. Explicitly, a second-order relaxation model, which shows a good balance between accuracy and simplicity, is established for analyzing the relationship between current and polarization voltage. Furthermore, considering the safe operation of the battery and hysteresis voltage issue, a 1 C bipolar-current pulse with 6-min duration is chosen for implementation. Experimental results on LiNiMnCoO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and LiNiCoAlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> batteries have proven the effectiveness of the proposed method, which can reduce up to 90% (depending on SOC level) of the time as compared with the conventional method.

An Improved Gated Recurrent Unit Network Model for State-of-Charge Estimation of Lithium-Ion Battery

An accurate state-of-charge (SOC) can not only provide a safe and reliable guarantee for the entirety of equipment but also extend the service life of the battery pack. Given that the chemical reaction inside the lithium-ion battery is a highly nonlinear dynamic system, obtaining an accurate SOC for the battery management system is very challenging. This paper proposed a gated recurrent unit recurrent neural network model with activation function layers (GRU-ATL) to estimate battery SOC. The model used deep learning technology to establish the nonlinear relationship between current, voltage, and temperature measurement signals and battery SOC. Then the online SOC estimation was carried out on different testing sets using the trained model. The experiments in this paper showed that the GRU-ATL network model could realize online SOC estimation under different working conditions without relying on an accurate battery model. Compared with the gated recurrent unit recurrent neural (GRU) network model and long short-term memory (LSTM) network model, the GRU-ATL network model had more stable and accurate SOC prediction performance. When the measurement data contained noise, the experimental results showed that the SOC prediction accuracy of GRU-ATL model was 0.1–0.4% higher than the GRU model and 0.3–0.7% higher than the LSTM model. The mean absolute error (MAE) of SOC predicted by the GRU-ATL model was stable in the range of 0.7–1.4%, and root mean square error (RMSE) was stable between 1.2–1.9%. The model still had high prediction accuracy and robustness, which could meet the SOC estimation in complex vehicle working conditions.