Thevenin Equivalent Circuit Model Research Articles

Study on the parameter identification of lithium-ion battery model under high-rate pulse discharge conditions

With the rapid development of the new energy sector and lithium-ion (Li-ion) battery technologies, using Li-ion batteries with high energy density and high discharge rate to form the primary energy subsystem can further improve the compactness and miniaturization level of pulsed power systems. In traditional electric power systems, Li-ion batteries normally operate under the discharge condition of low current and long time. However, as the main power source of pulsed power systems, it is required that Li-ion batteries should have the capability for high-rate pulse discharge. To ensure the safe and reliable operation of the battery energy storage system, it is necessary to conduct the parameter identification of the Li-ion battery model to establish an accurate pulse discharge model under such working conditions. This paper focuses on the discharge characteristics of a cylindrical high-rate single Li-ion battery with a capacity of 3 Ah. At a 20 C rate, the discharge data were obtained when the pulse repetition frequency was 10 Hz and the duty cycle was 90%. By using the mathematical expressions of the Thevenin equivalent circuit model, the recursive relationship of the circuit parameters was obtained, and the parameter identification of the battery model was conducted based on the experimental data by using the genetic algorithm. The results show that the fitting accuracy of the parameter identification reaches 0.9995, indicating the high precision of the model for the Li-ion battery. This work provides a significant reference for the modeling and parameter identification of Li-ion batteries under high-rate pulse discharge conditions.

SOC and SOH state estimation of lithium battery based on ffrls and kalman filter

Abstract In the energy storage System, the Battery Management System (BMS) is responsible for the charge and discharge control and energy balance control of the lithium battery, and the accuracy of lithium battery state estimation is directly affected by the control effect of BMS. In order to ensure the normal operation of lithium batteries, this paper selects the State of Charge (SOC) and State of Health (SOH) of lithium batteries as the research object and accurately estimates the SOC and SOH of lithium batteries as the research goal. The equivalent circuit model based on lithium battery is established, and the identification model parameters are based on the recursive least squares method with forgetting factor. Based on the Thevenin equivalent circuit model, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are used to estimate the SOC of the battery, respectively. FFRLS and Double Extended Kalman Filter (DEKF) are used to estimate the ohm internal resistance in the equivalent model based on lithium battery, and then the SOH is estimated.

Real-Time Online Estimation Technology and Implementation of State of Charge State of Uncrewed Aerial Vehicle Lithium Battery

The SOC estimation of UAV lithium batteries plays a crucial role in the mission planning and safe flight of UAVs. Aiming at existing UAV lithium battery SOC estimation problems, such as low estimation accuracy and poor real-time performance, a real-time online estimation scheme for UAV lithium battery SOC is proposed. A model-based approach is adopted to establish an SOC estimation model on the basis of the Thevenin equivalent circuit model, and a UAV lithium battery online monitoring device is developed to monitor the current and voltage of the UAV lithium battery in real time and import the data into the SOC estimation model in real time for calculation. Using the developed online monitoring device, the current and voltage of the lithium UAV battery are monitored in real time, and the data are imported into the SOC estimation model in real time for calculation, realizing the real-time online estimation of the SOC of the lithium UAV battery. The experimental results show that the program can realize the real-time online estimation of UAV lithium battery SOC, and the estimation error is less than 3%, which meets the requirements of online estimation accuracy of the UAV lithium battery SOC.

A Novel Redacted Extended Kalman Filter and Fuzzy Logic-Based Technique for Measurement of State-of-Charge of Lithium-Ion Battery

Abstract This paper presents a novel technique based on an adaptive approach of redacted extended Kalman filter (REKF) assimilating fuzzy logic features for measuring the state-of-charge (SoC) of lithium-ion batteries. Accurately determining SoC is crucial for maximizing battery capacity and performance. However, existing extended Kalman filtering algorithms suffer from issues such as inadequate noise resistance and noise sensitivity, as well as difficulties in selecting the forgetting factor. The aforementioned REKF technique addresses these challenges adequately for accurate measurement of SoC. The proposed method involves establishing a Thevenin equivalent circuit model and using the recursive least squares with forgetting factor (RLSFF) to identify model parameters. Furthermore, an evaluation factor is established, and to adaptively adjust the value of the forgetting factor, fuzzy control is utilized, which enhances the extended Kalman filtering algorithm with noise adaptive algorithm features to estimate the SoC accurately. This modified algorithm considers the identification results from the parameter estimation step and executes them circularly to achieve precise SoC estimation. Results demonstrate that the proposed method has excellent robustness and estimation accuracy compared to other filtering algorithms, even under variable working conditions, including a wide range of state-of-health (SOH) and temperature. The proposed method is expected to enhance the performance of battery management systems for various applications.

A Novel Dynamic Li-Ion Battery Model for the Aggregated Charging of EVs

Implementing successful aggregated charging strategies for electric vehicles to participate in the wholesale market requires an accurate battery model that can operate at scale while capturing critical battery dynamics. Existing models either lack precision or pose computational challenges for fleet-level coordination. To our knowledge, most of the literature widely adopts battery models that neglect critical battery polarization dynamics favoring scalability over accuracy, donated as constant power models (CPMs). Thus, this paper proposes a novel linear battery model (LBM) intended specifically for use in aggregated charging strategies. The LBM considers battery dynamics through a linear representation, addressing the limitations of existing models while maintaining scalability. The model dynamic behavior is evaluated for the four commonly used lithium-ion chemistries in EVs: lithium iron phosphate (LFP), nickel manganese cobalt (NMC), lithium manganese oxide (LMO), and nickel cobalt aluminum (NCA). The results showed that the LBM closely matches the high-fidelity Thevenin equivalent circuit model (Th-ECM) with substantially improved accuracy over the CPM, especially at higher charging rates. Finally, a case study was carried out for bidding in the wholesale energy market, which proves the ability of the model to scale.

Elman neural network and Thevenin equivalent circuit model based multi-measurement Kalman filter for SOC estimation

Elman neural network and Thevenin equivalent circuit model based multi-measurement Kalman filter for SOC estimation

An Adaptive Peak Power Prediction Method for Power Lithium-Ion Batteries Considering Temperature and Aging Effects

The battery power state (SOP) is the basic indicator for the Battery management system (BMS) of the battery energy storage system (BESS) to formulate control strategies. Although there have been many studies on state estimation of lithium-ion batteries (LIBs), aging and temperature variation are seldom considered in peak power prediction during the whole life of the battery. To fill this gap, this paper aims to propose an adaptive peak power prediction method for power lithium-ion batteries considering temperature and aging is proposed. First, the Thevenin equivalent circuit model is used to jointly estimate the state of charge (SOC) and SOP of the lithium-ion power battery, and the variable forgetting factor recursive least squares (VFF-RLS) algorithm and extended Kalman filter (EKF) are utilized to identify the battery parameters online. Then, multiple constraint parameters including current, voltage, and SOC were derived, considering the dependence of the polarization resistance of the battery on the battery current. Finally, the verification experiment was carried out with LiFePO4 battery. The experimental results under FUDS operating conditions show that the maximum SOC estimation error is 1.94%. And the power prediction errors at 20%, 50%, and 70% SOC were 5.0%, 8.1% and 4.5%, respectively. Our further work will focus on the joint estimation of battery state to further improve the accuracy.

State of charge estimation of ternary lithium-ion batteries at variable ambient temperatures

Among the factors that affect lithium-ion batteries, ambient temperature has a great influence on the charge and discharge rate, general battery performance, and storage capacity of the battery, hence accurate state of charge (SOC) estimation over a wide range of temperatures is essential and necessary. In this paper, a Second-order Thevenin equivalent circuit model is established with ambient temperature compensation over varying ambient temperature conditions. An improved Fixed Range Forgetting Factor-Adaptive Extended Kalman Filtering (FRFF-AEKF) algorithm with the Saga-Husa Adaptive filter (SHAF) is proposed for the accurate estimation of SOC at variable ambient temperature. The temperatures −10°C, 10 °C, 25 °C, and 40 °C are set to depict low, normal, and high ambient temperatures in which lithium-ion batteries in electric vehicles (EVs) and most electronic devices usually operate. Tests conducted include the hybrid pulse power characterization (HPPC) for obtaining data required for parameterization, and for SOC estimation and verification, the Beijing Bus Dynamic stress (BBDST). The object of the tests was a ternary lithium-ion battery representing those used in electric vehicles (EVs). To improve adaptability, reduced noise, and achieve faster convergence with increased accuracy, the range of forgetting factor is fixed between a variable range of 0.997–1. To verify the performance of the proposed algorithm under varying conditions and different ambient temperatures, the SOC estimation result was compared with that of the adaptive extended Kalman filtering (AEKF) algorithm. The results show that the proposed improved algorithm implemented with the established Second-order Thevenin equivalent model has a 1.1 % better estimation accuracy compared to the results of the AEKF algorithm. This confirms that the proposed method can achieve accurate SOC estimation and is adaptive to variable ambient temperatures.

Regrouping strategy of retired batteries considering SOC consistency

This paper proposes a method for retired batteries based on SOC consistency matching. This method takes the SOC consistency of the battery pack as the standard, which calculates the model parameter matching relationship to optimize the performance of the pack. Based on Thevenin equivalent circuit model, the mathematical model of lithium ion battery is established and the model is parameterized. Additionally, a battery pack reconfiguration criterion based on SOC consistency is proposed to reveal the mapping relationship between cell parameters and battery pack SOC consistency. Finally, the battery parameters are identified by the recursive least squares (RLS) algorithm to select two groups of batteries. Dynamic and constant current tests are performed on battery packs with different topologies, which are used to verify the feasibility of the proposed method. The experimental results show that the proposed reorganization scheme can better ensure the consistency of the SOC of the battery pack during charging and discharging.

State of charge estimation of lithium-ion battery based on improved forgetting factor recursive least squares-extended Kalman filter joint algorithm

In order to solve the problem that forgetting factor recursive least squares (FFRLS) is prone to abnormal jitter and even divergence under complex working conditions, improved forgetting factor recursive least squares based on dynamic constraint and parameter backtracking is proposed. A joint algorithm of improved forgetting factor recursive least squares and extended Kalman filter (EKF) is used to estimate the state of charge (SOC) of lithium-ion battery. Firstly, parameters of Thevenin equivalent circuit model are identified on-line by the improved FFRLS considering dynamic constraint and parameter backtracking, and then the SOC of lithium-ion battery is estimated by extended Kalman filter. The results show that the improved forgetting factor recursive least squares has high accuracy of battery model parameters identification and the joint algorithm also has high accuracy and robustness of SOC estimation under dynamic stress test (DST) condition, the maximum absolute SOC estimation error is 2.49 % and the average absolute SOC estimation error is 1.39 %.

SOC Estimation Based on Hysteresis Characteristics of Lithium Iron Phosphate Battery

In order to improve the estimation accuracy of the state of charge (SOC) of lithium iron phosphate power batteries for vehicles, this paper studies the prominent hysteresis phenomenon in the relationship between the state of charge and the open circuit voltage (OCV) curve of the lithium iron phosphate battery. Through the hysteresis characteristic test of the battery, the corresponding SOC-OCV data when the battery is charged or discharged from different SOC states are analyzed. According to the approximation trend of the hysteresis main loop curve by the data points, a differential equation model for approximately solving the charge or discharge hysteresis small loop curve under any SOC state is established, and the adjustment parameters of the model are analyzed and debugged in sections. Then, based on the second-order Thevenin equivalent circuit model, the forgetting factor recursive least squares method is used to identify the model parameters online. When deriving the relationship between the OCV and SOC, according to the state of charge and discharge and the current SOC value, the approximate model of the real hysteresis small loop curve in the current state is solved in real time, and the extended Kalman recursion algorithm is substituted to correct the corresponding relationship between the OCV and SOC. Finally, the integrated forgetting factor recursive least squares online parameter identification and extended Kalman filter to correct the SOC-OCV hysteresis relationship in real time considering the hysteresis characteristics are used to complete the real-time estimation of the SOC of the lithium iron phosphate battery. The synthesis algorithm proposed in this paper and the Kalman filter algorithm without considering the hysteresis characteristics are compared and verified under the Dynamic Stress Test (DST) data. Based on the method proposed in this paper, the maximum error of terminal voltage is 0.86%, the average error of terminal voltage is 0.021%, the root mean square error (RMSE) of terminal voltage is 0.042%, the maximum error of SOC estimation is 1.22%, the average error of SOC estimation is 0.41%, the average error of SOC estimation is 0.41%, and the RMSE of SOC estimation is 0.57%. The results show that the comprehensive algorithm proposed in this paper has higher accuracy in both terminal voltage following and SOC estimation.

Electrochemical Impedance Spectroscopy Setup based on Standard Measurement Equipment

The approach of electrochemical impedance spectroscopy is widely used to analyze electrochemical systems such as batteries and fuel cells. The majority of commercial spectroscopes is however limited to the investigation of devices under test at laboratory scale. In this paper the development of a setup performing impedance spectroscopy of commercial lithium-ion battery cells and complete packs up to 42 V and 10S4P configuration is demonstrated which is entirely based on standard measurement equipment. Galvanostatic AC excitation of up to 5A peak-to-peak can be reached. The obtained impedance spectra qualitatively match the theoretical expectations and reference results from literature. Acquired results can be successfully fitted to a second-order Thevenin equivalent circuit model without requirement of specialized analysis software. OriginPro is used as an example for the presented setup. A similar sensitivity towards external factors such as temperature and probe contacting as it applies for commercial devices is observed. The described setup can be reproduced in most electrical laboratories with similar equipment and the application scenario is not limited to batteries. This gives access to a powerful analysis tool complementing commercial impedance spectroscopy devices by extending measurement ranges towards higher voltage and excitation current as well as lower impedance.

Hava Aracı Batarya Hücresinin Modellenmesi

Batteries, which are used as energy storage tools, are widely used today and are of great importance. Batteries are used and developed in many different technologies. Today, batteries appear in many areas such as computers, electrical vehicles, electronic devices and aircraft. Since they are used in many different and various fields, battery preferences can be determined according to the purpose of use. In this study, the properties and usage purposes of nickel-cadmium (Nickel-Cadmium, Ni-Cad) type batteries used in aircraft are emphasized. The modeling of the Ni-Cad battery cell at the time of charge and discharge was carried out using MATLAB/Simulink. While modeling, Thevenin equivalent circuit model was used. Within the scope of this study, experimental test data were obtained from the workshop where charge and discharge tests of Ni-Cad battery cells were carried out. The graphs obtained from those experimental test data the modeling performed were compared. As a result of the comparison, it was seen that successful results were obtained close to each other. With the modeling made in this study, a faster and more reliable system was created and it was thought that manufacturers could easily access data for testing purposes.

An extended Kalman filter based SOC estimation method for Li-ion battery

In recent years, the global environmental pollution and energy crisis are becoming more and more serious. The Li-ion battery is widely used in vehicles due to long cycle life and high energy density. The state of charge (SOC) of Li-ion battery is an important indicator. The accurate estimation of SOC can ensure the safe operation of Li-ion battery. However, the traditional estimation method, the ampere-hour integration method, has a cumulative error and cannot maintain good results for a long time in an operating environment with the Gaussian noise. To this end, this paper firstly applies Thevenin equivalent circuit model of a battery to establish estimation model, and it can reflect the working state of the battery. Then, the extended Kalman filtering algorithm is employed to solve the estimation error caused by Gaussian noise. Finally, the test system is built in MATALAB/Simulink to investigate the performance of the proposed method. Simulation results show that the proposed method achieves better performance, and it has higher estimation accuracy in comparison with traditional methods under different working conditions.

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.

An Adaptive State of Charge Estimation Method of Lithium-ion Battery Based on Residual Constraint Fading Factor Unscented Kalman Filter

It is crucial to conduct highly accurate estimation of the state of charge (SOC) of lithium-ion batteries during the real-time monitoring and safety control. Based on residual constraint fading factor unscented Kalman filter, the paper proposes an SOC estimation method to improve the accuracy of online estimating SOC. A priori values of terminal voltage were fitted using cubic Hermite interpolation. In combination with the Thevenin equivalent circuit model, the method of adaptive forgetting factor recursive least squares is used to identify the model parameters. To address the problem of the UKF method strongly influenced by system noise and observation noise, the paper designs an improved method of residual constrained fading factor. Finally, the effectiveness of this method was verified by the test of Hybrid Pulse Power Characteristic and Beijing Bus Dynamic Stress Test. Results show that under HPPC conditions, compared with other methods, the algorithm in the paper estimates that the SOC error of the battery remains between -0.38% and 0.948%, reducing the absolute maximum error by 51.5% at least and the average error by 62.7% at least. Moreover, under the condition of Beijing Bus Dynamic Stress Test the algorithm estimates the SOC error of the battery stays between -0.811% and 0.526%, the SOC estimation errors are all within 0.2% after operation of ten seconds. Compared with other methods, the absolute maximum error can be reduced by 42.7% at least, the average error is reduced by 95% at least. Finally, the test proves that the method is of higher accuracy, better convergence and stronger robustness.

Kalman Filter Estimation of Lithium Battery SOC Based on Model Capacity Updating

High-precision estimation of lithium battery SOC can effectively optimize vehicle energy management, improve lithium battery safety protection, extend lithium battery cycle life, and reduce new energy vehicle costs. Based on the forgetting factor recursive least square method (FFRLS), Thevenin equivalent circuit model and Singular Value Decomposition-Unscented Kalman Filter (SVD-UKF), the SVD-UKF combined lithium battery SOC estimation algorithm with model capacity update is proposed, aiming at further improving the SOC estimation accuracy of lithium battery. The parameter identification of Thevenin model is studied by using the forgetting factor recursive least square method. To overcoming the shortcomings of Kalman filter linearization error and non-positive definite covariance matrix, the singular value decomposition unscented Kalman filter algorithm is proposed. It is worth mentioning that in order to consider the impact of battery available capacity attenuation on the estimation of lithium battery SOC, the model capacity update algorithm is used to optimize the model parameters and state joint estimation algorithm based on FFRLS & SVD-UKF. Verified by simulation and lithium battery test, the results show that the SVD-UKF algorithm based on model capacity update can accurately estimate the SOC of lithium battery in real time with the available capacity of lithium battery continuous attenuation. The purpose of improving the accuracy of SOC estimation of lithium batteries is achieved.

State-of-charge estimation for the lithium-ion battery based on adaptive extended Kalman filter using improved parameter identification

The state of charge(SOC) of lithium-ion battery is an essential parameter of battery management system. Accurate estimation of SOC is conducive to give full play to the capacity and performance of the battery. For the problems of selection of forgetting factor and poor robustness and susceptibility to the noise of extended Kalman filtering algorithm, this paper proposes a SOC estimation method for the lithium-ion battery based on adaptive extended Kalman filter using improved parameter identification. Firstly, the Thevenin equivalent circuit model is established and the recursive least squares with forgetting factor(FFRLS) method is used to achieve the parameter identification. Secondly, an evaluation factor is defined, and fuzzy control is used to realize the mapping between the evaluation factor and the correction value of forgetting factor, so as to realize the adaptive adjustment of forgetting factor. Finally, the noise adaptive algorithm is introduced into the extended Kalman filtering algorithm(AEKF) to estimate the SOC based on the identification results, which is applied to the parameter identification at the next time and executed circularly, so as to realize the accurate estimation of SOC. The experimental results show that the proposed method has good robustness and estimation accuracy compared with other filtering algorithms under different working conditions, state of health(SOH) and temperature.

A novel hybrid equivalent circuit model for lithium-ion battery considering nonlinear capacity effects

In this paper, a novel hybrid equivalent circuit model for lithium-ion battery. The proposed equivalent circuit model of lithium-ion battery is based on Thevenin equivalent circuit model, and a state-of-charge (SOC) part is added into the model to improve the model performance. In the proposed model, the battery capacity is divided into available capacity and unavailable capacity, which can well reflect the rated capacity effect when the battery is working, the recovery effect when the battery is not working and the self-discharge effect at all times. At the same time, a new definition of the SOC is given. The SOC value of the battery is estimated in real time through the model of the charged state part, and the one-to-one correspondence between SOC and open circuit voltage is established. Besides, the second-order polarized RC network in Thevenin model is improved to the third-order RC network, and the third-order RC network is endowed with practical physical significance, to reflect the polarization effect of the battery more accurately. Finally, Simulink simulation and experimental results have verified the correctness of the proposed model.

SOC estimation for lithium‐ion batteries based on a novel model

Lithium-ion batteries (LIBs) are widely used in electric vehicles because of their high energy density and less pollution. As an important parameter of the battery management system, accurate estimation of the state of charge (SOC) of the battery can ensure the energy distribution and safe use of the battery. This paper obtains better estimation accuracy from four aspects. First, the battery model is established via Thevenin equivalent circuit model, and the parameters are identified by the forgetting factor recursive least squares. Second, the influence of dual extended Kalman filter on SOC estimation is analysed, a novel algorithm-based improved dual Kalman filter is proposed. Besides, to reduce the influence of the system noise on the estimation results, an adaptive intelligent algorithm is applied to promote the accuracy of SOC estimation. Finally, compared with the estimated SOC results of the traditional algorithm, the experimental results show the effectiveness of the algorithm.