State Of Charge Estimation Algorithm Research Articles

Estimation of battery open-circuit voltage and state of charge based on dynamic matrix control - extended Kalman filter algorithm

State of Charge (SOC) estimation is one of the most important functions of the battery management system for new energy vehicles. Extended Kalman Filter (EKF) algorithm has been widely used in SOC estimation of lithium-ion batteries (LiBs). However, the model parameters in the SOC estimation algorithm change with the aging of the battery, which makes EKF unable to obtain accurate estimation results. Because of these defects, a battery model is built based on the second-order RC equivalent circuit model. The parameters of the LiB model are identified by an off-line test and the battery simulation model is calibrated. Then, based on the simulation model, the influence of Open Circuit Voltage (OCV) deviation on SOC estimation accuracy of the EKF algorithm is quantitatively analyzed. The results show that the deviation of OCV will affect the accuracy of SOC estimation by the EKF algorithm. When the OCV deviation reaches 15 mV, the SOC estimation error will reach 5%. Subsequently, a method of updating model parameters based on the Dynamic Matrix Control (DMC) algorithm is proposed. And the DMC-EKF algorithm is used to estimate OCV and SOC. The results show that after the DMC algorithm is used to linearize the RC network, the identified OCV parameter deviation is <10 mV, and the SOC deviation estimated by the DMC- EKF algorithm is <5%, which can meet the application requirements. The EKF algorithm can estimate the SOC more accurately after updating the OCV by the DMC algorithm. Compared with EKF algorithm and UKF algorithm without online OCV updating, DMC-EKF algorithm reduces the maximum deviation of SOC estimation by at least 2%. The proposed DMC-EKF algorithm has good accuracy and robustness.

Verification Platform of SOC Estimation Algorithm for Lithium-Ion Batteries of Electric Vehicles

As one of the core technologies of electric vehicles (EVs), the state of charge (SOC) estimation algorithm of lithium-ion batteries is directly related to the performance of the battery management system (BMS). Before EVs are put into the market, the SOC estimation algorithm must be tested and verified to ensure the reliability of the BMS and the safe operation of EVs. Therefore, this paper establishes a lithium-ion batteries’ SOC estimation algorithm verification platform for the comprehensive performance evaluation and verification of the new SOC estimation algorithm. In addition, there are two schemes, including real-time SOC estimation verification and offline SOC estimation verification can be selected, which improve the reliability and efficiency of verification. Firstly, the design idea of the verification platform (the research and development purpose, functional requirements, and the overall design scheme) is introduced in detail. Secondly, the modular design idea is used to design the hardware structure of the verification platform, which mainly includes the BMS host module, BMS slave module, battery charger module, and electronic load module. Finally, the software system, including the communication architecture, the SOC reference standard and evaluation indexes of the algorithm, and the upper computer function and implementation is designed to realize the functions of the verification platform.

State of charge estimation for lithium-ion batteries connected in series using two sigma point Kalman filters

This paper proposes a method to estimate state of charge (SoC) for Lithium-ion battery pack (LIB) with 𝑁 series-connected cells. The cell’s model is represented by a second-order equivalent circuit model taking into account the measurement disturbances and the current sensor bias. By using two sigma point Kalman filters (SPKF), the SoC of cells in the pack is calculated by the sum of the pack’s average SoC estimated by the first SPKF and SoC differences estimated by the second SPKF. The advantage of this method is the SoC estimation algorithm performed only two times instead of 𝑁 times in each sampling time interval, so the computational burden is reduced. The test of the proposed SoC estimation algorithm for 7 samsung ICR18650 Lithium-ion battery cells connected in series is implemented in the continuous charge and discharge scenario in one hour time. The estimated SoCs of the cells in the pack are quite accurate, the 3-sigma criterion of estimated SoC error distributions is 0.5%.

Continual Refoircement Learning Using Real-World Data for Intelligent Prediction of SOC Consumption in Electric Vehicles

The accelerated migration towards electric vehicles (EV) presents several problems to solve. The main aspect is the management and prediction of the state of charge (SOC) in real long-range routes of different variations in altitude for a more efficient energy consumption and vehicle recharge plan. This paper presents the implementation of a new algorithm for SOC estimation based on continuous learning and meta-experience replay (MER) with reservoir sample. It combines the reptile meta-learning algorithm with the experience replay technique for stabilizing the reinforcement learning. The proposed algorithm considers several important factors for the prediction of the SOC in EV such as: speed, travel time, route altimetry, consumed battery capacity, regenerated battery capacity. A modified principal components analysis is used to reduce the dimensionality of the route altimetry data. The experimental results show an efficient estimation of the SOC values and a convergent increase in knowledge while the vehicle travels the routes.

An execution time optimized state of charge estimation method for lithium-ion battery

State of charge (SOC) estimation is one of the most important outputs of the battery management system (BMS). There are several algorithms for SOC estimation. Each method has advantages like self-correction ability and disadvantages like computational complexity for an embedded system. In the first part of this article, different estimation techniques are reviewed and compared. Particular emphasis was placed on two methods: Coulomb Counting (CC) and Sigma Point Kalman Filter (SPKF). These two methods are analyzed in terms of several aspects such as tolerance to noisy signal, recovery ability from an intentional SOC distortion as well as estimation accuracy comparison. Also, an embedded development kit is used to analyze execution time of each method. The results show that using SPKF alone is a computationally expensive method especially for a battery pack with a high number of cells in series. On the other hand, using CC alone could be vulnerable to SOC distortion and noisy measurement signals and this may lead to inaccurate predictions. Based on these facts, a hybrid approach has been proposed to take advantage of each method’s superiority. The emphasis in this paper is on execution step time analyses under different conditions and drive cycles. On top of this article, further studies may pave the way for more cost effective solutions like downsizing of the processor.

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.

A Robust Algorithm for State-of-Charge Estimation under Model Uncertainty and Voltage Sensor Bias

Accurate estimation of the state of charge (SOC) of zinc–nickel single-flow batteries (ZNBs) is an important problem in battery management systems (BMSs). A nonideal electromagnetic environment will usually cause the measured signal to contain nonnegligible noise and bias. At the same time, due to the influence of battery ageing, environmental temperature changes, and a complex reaction mechanism, it is difficult to establish a very accurate system model that can be applied to various complex working conditions. The unscented Kalman filter (UKF) is a widely used SOC estimation algorithm, but the UKF will reduce the estimation accuracy and divergence under the influence of inaccurate model and sensor errors. To improve the performance of the UKF, a robust desensitized unscented Kalman filter (RDUKF) is proposed to realize an accurate SOC estimation of batteries in the context of different disturbances. Then, the proposed method is applied to cases of error interference, such as Gaussian noise, voltage sensor drift, an unknown initial state, and inaccurate model parameters. The simulation and experimental results show that compared with the standard UKF algorithm, the proposed estimation algorithm can effectively suppress the influence of various errors and disturbances and achieve higher accuracy and robustness.

Research on Co-Estimation Algorithm of SOC and SOH for Lithium-Ion Batteries in Electric Vehicles

The accurate estimation of the state of charge (SOC) and state of health (SOH) is of great significance to energy management and safety in electric vehicles. To achieve a good trade-off between real-time capability and estimation accuracy, a collaborative estimation algorithm for SOC and SOH is presented based on the Thevenin equivalent circuit model, which combines the recursive least squares method with a forgetting factor and the extended Kalman filter. First, the parameter identification accuracy is studied under a dynamic stress test (DST) and the federal urban driving schedule (FUDS) test at different ambient temperatures (0 °C, 25 °C, and 45 °C). Secondly, the FUDS test is used to verify the SOC estimation accuracy. Thirdly, two batteries with different aging degrees are used to validate the proposed SOH estimation algorithm. Subsequently, the accuracy of the SOC estimation algorithm is studied, considering the influence of updating the SOH. The proposed SOC estimation algorithm can achieve good performance at different ambient temperatures (0 °C, 25 °C, and 45 °C), with a maximum error of less than 2.3%. The maximum error for the SOH is less than 4.3% for two aged batteries at 25 °C, and it can be reduced to 1.4% after optimization. Furthermore, calibrating the capacity as the SOH changes can effectively improve the SOC estimation accuracy over the whole battery life.

State of Charge Estimation for Lithium-ion Batteries using Extreme Learning Machine and Extended Kalman Filter

State of charge (SoC) estimation is one of the most important functions for battery management systems (BMSs). Due to the complex electrochemical characteristics of Lithium-ion batteries (LIBs), accurate SoC estimation remain challenges. To take full advantage of the widely used model-based methods and data-driven methods, an extreme learning machine-extended Kalman filter (ELM-EKF)-based method is proposed for SoC estimation in this paper. The ELM is utilized to establish an accurate LIBs model first. Then, the trained ELM model is combined with the EKF algorithm for SoC estimation. The proposed ELM-EKF-based SoC estimation method is validated and compared with the traditional equivalent circuit model-EKF (ECM-EKF)-based method under Federal Urban Driving Schedule (FUDS) driving cycles at three different temperatures. The results prove that the ELM model have better voltage-tracking capability than the ECM model while the ELM-EKF-based SoC estimation algorithm can achieve higher estimation accuracy than the ECM-EKF-based method.

State of charge estimation for liquid metal battery based on an improved sliding mode observer

Electrochemical energy storage is becoming one of the most promising solution for renewable energy integration. Liquid metal battery is a prospective battery chemistry for stationary energy storage due to its low cost and long lifespan. However, the flat voltage platform and low working voltage easily introduce relative errors, resulting in challenges in battery state of charge (SOC) estimation. Meanwhile, practical applications of liquid metal batteries require efficient SOC estimation algorithms for massively parallel computing. Thus, in this paper, an improved sliding mode observer (ISMO) is proposed for liquid metal battery SOC estimation to meet the challenges. Firstly, based on a combined equivalent circuit model, the forgetting factor recursive least square algorithm is utilized to identify model parameters in the whole working range. Secondly, a direct differentiation method is put forward to deal with the linearization between the open circuit voltage and the SOC. Finally, a novel adaptive law is proposed to accelerate the convergence, restrict the probable large chattering and improve the estimation accuracy of the algorithm. Compared to the conventional model-based methods, the proposed ISMO exhibits faster convergence, higher accuracy, stronger robustness and lower computational cost in simulations, which indicates an industrialization prospect.

A State of Charge Estimation of The Lithium-Ion Batteries Based on Reduced-Order Unscented Kalman Filtering Method

State of Charge (SOC) represents the available battery capacity and is one of the most important states that need to be monitored to optimize the performance and extend the lifetime of lithium-ion batteries. SOC estimation is a challenging task hindered by considerable changes in battery characteristics over its lifetime due to aging and distinct nonlinear behavior. This paper compares two of the basic methods and algorithms for SOC estimation of lithium-ion batteries (LIBs) focusing on the description of the two techniques in a test experiment and the elaboration of their differences for use in battery management systems (BMS) applications. A Reduced-order unscented Kalman filter method is used for estimation and tracking to realizer real-time high-precision estimation of lithium-ion battery state of charge. Experimental tests are carried out with a lithium-ion battery cell for model and state estimation validations. Many researchers have proposed different methods of estimating SOC that raised the challenge of establishing a relationship between the accuracy and robustness of the method. The experimental results of the OCV-SOC estimation method, Hybrid Pulse Power Characterization (HPPC) test, and Beijing Bus Dynamic Stress Test (BBDST) working condition method are analyzed. The error of SOC estimation based on the established Thevenin RC modeling using the Reduced-order-unscented Kalman filter is less than 0.3%. The result from the use of the reduced-order unscented Kalman filtering algorithm proves that it has high accuracy in the state of charge estimation of the lithium-ion batteries. Keywords : lithium-ion battery, open-circuit voltage, state of charge estimation, battery management system, HPPC test, reduced-order unscented Kalman filter DOI: 10.7176/JETP/11-6-05 Publication date: December 30 th 2021

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.

A Particle-Swarm-Optimization-Based Approach for the State-of-Charge Estimation of an Electric Vehicle When Driven Under Real Conditions

Recent developments in lithium-ion (Li-ion) storage technology have enabled a revolution in the automotive industry. Fully electric vehicles (EVs) operate under the most diverse combination of driving and environmental conditions affecting the autonomy range. In other words, an equal state-of-charge (SOC) on two same model EV does not mean the same traveling distance since the conditions such as the state-of-health (SOH) of the battery, type of driver and even the type of route will influence the EV performance. Typically, SOC estimation algorithms are proposed and validated under controlled laboratory conditions. However, when real conditions are present, it is necessary to incorporate new tools capable of handling the diverse variability present in all the conditions. For instance, the topography of the route influences the current that the battery pack delivers, and the performance on the same route can be affected by the SOH. One of the main concerns for EV owners is that once a battery pack is installed, it becomes almost impossible to perform laboratory tests under controlled conditions. This paper proposes a novel approach to estimate the SOC by extending an existing SOC model (obtained in laboratory conditions) with the novelty of the assistance of Particle-Swarm-Optimization (PSO) to estimate the model parameters using real EV driving data. The data was obtained by a real-driving experiment, which consists on driving the EV in a complete discharge cycle on a highway. During this experiment, the initial SOC was at 100\%, and the idea was to discharge the battery pack driving through a highway where the driving conditions are almost uniform making it possible to characterize the SOC curve. Then, PSO is used to estimate the model parameters, and afterwards the model is validated in different types of routes. The obtained results show that the proposed approach can estimate the SOC satisfactorily. In this regard, this type of real-driving experiment can be performed by any driver, and by combining the particular results with the proposed approach, the users can personalize the SOC estimation model to their vehicles, and even more, create their own knowledge base of their EV performance through time. Therefore, the real-driving experiment can be replicated when needed to update the model parameters, thus allowing a better understanding of the actual SOH of the battery pack. Furthermore, by combining the obtained model with the elevation profile of a given route, the user can assess where to stop in case that a recharge is necessary.

Lithium‐ion battery state‐of‐charge estimation of an order‐reduced physics‐based model in electric vehicles considering erroneous initialization

Intelligent battery management systems (BMSs) require immediate and precise state of charge (SoC) estimation of the lithium-ion cell for efficient use in electric vehicles (EVs). To solve the problem of real-time SoC estimation for physics-based lithium-ion cell models in BMSs, rigorous physics-based models are required to be reasonably order-reduced. In this paper, an improved order-reduced physics-based model is proposed and validated with experimental data. Next, state equations of the reduced model are established by adopting finite difference approaches. Moreover, three reduced model-based estimators including the extended Kalman filter (EKF), the uniform reaching law sliding-mode observer (SMO-URL), and the exponential reaching law sliding-mode observer (SMO-ERL) are developed to estimate battery SoC by using input current and external measured voltage. To demonstrate the effectiveness of the proposed SoC estimation algorithms, their performances are evaluated and compared via experimentation under the hybrid pulse power characteristic (HPPC) test. The results show that the proposed order-reduced model-based SMO-ERL algorithm has faster convergence ability and higher estimation accuracy compared with the other two algorithms under incorrect SoC initial conditions.

A novel Fireworks Factor and Improved Elite Strategy based on Back Propagation Neural Networks for state-of-charge estimation of lithium-ion batteries

The state of charge (SOC) of Lithium-ion battery is one of the key parameters of the battery management system. In the SOC estimation algorithm, the Back Propagation (BP) neural network algorithm is easy to converge to the local optimal solution, which leads to the problem of low accuracy based on the BP network. It is proposed that the Fireworks Elite Genetic Algorithm (FEG-BP) is used to optimize the BP neural network, which can not only solve the problem of the traditional neural network algorithm that is easy to fall into the local maximum optimal solution but also solve the limitation of the traditional neural network algorithm. The searchability of the improved algorithm has been significantly enhanced, and the error has become smaller and the propagation speed is faster. Combining the experimental data of charging and discharging, the proposed FEG-BP neural network is compared with the traditional genetic neural network algorithm (GA-BP), and the results are analyzed. The results show that the standard BP neural network genetic algorithm predicts error within 7%, while FEG-BP reduces the error to within 3%.

State of Charge Estimation Algorithm Based on Fractional-Order Adaptive Extended Kalman Filter and Unscented Kalman Filter

Abstract Accurate estimation of state of charge (SOC) is the basis of battery management system. The fractional-order theory is introduced into the resistance-capacitance (RC)model of lithium battery, and adaptive genetic algorithm is used to identify the parameters of the RC model. Considering the changes of internal resistance and battery aging during battery discharge, the state of health (SOH) of the battery is estimated by unscented Kalman filter (UKF), and the values of internal resistance and maximum capacity of the battery are obtained. Finally, a novel estimation algorithm of lithium battery SOC based on SOH and fractional-order adaptive extended Kalman filter (FOAEKF) is proposed. An experimental system is set up to verify the effectiveness of the proposed algorithm. The experimental results show that, compared with the traditional SOC estimation algorithms, the proposed method has higher estimation accuracy, with the average error lower than 1% and the maximum error lower than 2%.

More intelligent and robust estimation of battery state-of-charge with an improved regularized extreme learning machine

State-of-charge (SOC) is the key parameter for battery management, and the accurate estimation of SOC is pretty important for the safe and stable operation of lithium batteries. This paper investigates a regularized extreme learning machine trained with the spectral Fletcher–Reeves algorithm and tuned with the beetle antennae search algorithm (BAS-SFR-RELM) for intelligent and robust SOC estimation. In the experiment section, the urban dynamometer driving schedule (UDDS) profile and the Los Angeles 92 (LA92) profile are performed on a battery test platform for data collection. In the simulation section, the root mean squared error (RMSE) and the mean absolute error (MAE) are adopted to evaluate the performance of the model. Compared with the linear regression (LR), the back propagation (BP) network, the multi-layer perceptron (MLP), and the long short-term memory (LSTM) network, the BAS-SFR-RELM method can efficiently obtain the optimal regularization coefficient to effectively prevent overfitting with faster convergence speed. Increasing the number of hidden neurons in the BAS-SFR-RELM appropriately can improve the SOC estimation precision. Implementing the BAS-SFR-RELM with the noise-added data set gives high robustness for SOC estimation

Lithium Battery SOH Monitoring and an SOC Estimation Algorithm Based on the SOH Result

Lithium batteries are the most common energy storage devices in items such as electric vehicles, portable devices, and energy storage systems. However, if lithium batteries are not continuously monitored, their performance could degrade, their lifetime become shortened, or severe damage or explosion could be induced. To prevent such accidents, we propose a lithium battery state of health monitoring method and state of charge estimation algorithm based on the state of health results. The proposed method uses four neural network models. A neural network model was used for the state of health diagnosis using a multilayer neural network model. The other three neural network models were configured as neural network model banks, and the state of charge was estimated using a multilayer neural network or long short-term memory. The three neural network model banks were defined as normal, caution, and fault neural network models. Experimental results showed that the proposed method using the long short-term memory model based on the state of health diagnosis results outperformed the counterpart methods.

State estimation based on least square support vector

As one of the important parameters of battery management system (BMS), accurate estimation of the state of charge (SOC) of lithium-ion battery (LIB) can ensure the safety of electric vehicles and improve the utilization rate of batteries. A new SOC estimation algorithm based LSSVM is applied. The battery parameters, including current and voltage, which are used as the inputs to estimate SOC. To promote the accuracy of SOC estimation, the SOC estimated at the previous time is taken as the feedback vector to estimate the SOC at the current time. The experimental results show that the proposed model can improve the estimation accuracy of SOC.

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.