Circuit Model Of Lithium-ion Battery Research Articles

Development and Evaluation of a Physicochemical Equivalent Circuit Model for Lithium-Ion Batteries

Physicochemical models of lithium-ion cells, like the Doyle Fuller Newman (DFN) model, are omnipresent in battery research and development as they provide crucial insight into the cell, while equivalent circuit models dominate the area of application-oriented models, where speed is paramount. In this work, we develop and analyze a model that combines the two approaches using equivalent circuits and the DFN theory. By using a generalized approach to equivalent circuits, we model the necessary electric and diffusional processes analogously. The developed model accounts for all physical processes and internal states contained in the standard DFN model. We investigate the impact of model discretization and compare the developed model to a reference DFN implementation. Agreement between the models for both the predicted cell voltage and internal states shows that the developed equivalent circuit model provides a physically meaningful description of a lithium-ion battery, thereby successfully combining the two main modeling approaches for lithium-ion batteries.

Identification of fractional-order equivalent circuit model of lithium-ion battery for improving estimation of state of charge

Accurate estimation of State of Charge (SOC) based on equivalent circuit model (ECM) of Lithium-ion batteries (LIBs) is an important research topic. Recent research has found that fractional-order model (FOM), as one kind of equivalent circuit model, can provide a better description of LIBs dynamics than the conventional integer-order ECMs. However, it is difficult to directly identify an FOM online. In this paper, a synergy of Beetle Antennae Search and Recursive Least Squares (BAS-RLS) is proposed to identify the parameters of an FOM for LIBs. Specifically, the BAS is adopted to determine the fractional order, while the remaining parameters of FOM are estimated via the well-established RLS algorithm. A comparison study will demonstrate that this method offers a similar modeling accuracy as the Particle Swarm Optimization (PSO), and the online estimated model is more accurate than offline estimated models. Based on the identified FOM, this article then explores the battery SOC estimation from two aspects: initial value effect of the SOC and the comparison of multiple estimation algorithms, thus verifying the advantage of the proposed method for LIBs modeling and SOC estimation.

BattX: An equivalent circuit model for lithium-ion batteries over broad current ranges

Advanced battery management is as important for lithium-ion battery systems as the brain is for the human body. Its performance is based on the use of fast and accurate battery models. However, the mainstream equivalent circuit models and electrochemical models have yet to meet this need well, due to their struggle with either predictive accuracy or computational complexity. This problem has acquired urgency as some emerging battery applications running across broad current ranges, e.g., electric vertical take-off and landing aircraft, can hardly find usable models from the literature. Motivated to address this problem, we develop an innovative model in this study. Called BattX, the model is an equivalent circuit model that draws comparisons to a single particle model with electrolyte and thermal dynamics, thus combining their respective merits to be computationally efficient, accurate, and physically interpretable. The model design pivots on leveraging multiple circuits to approximate major electrochemical and physical processes in charging/discharging. Given the model, we develop a multipronged approach to design experiments and identify its parameters in groups from experimental data. Experimental validation proves that the BattX model is capable of accurate voltage prediction for charging/discharging across low to high C-rates.

A comprehensive equivalent circuit model for lithium-ion batteries, incorporating the effects of state of health, state of charge, and temperature on model parameters

The equivalent circuit model (ECM) is a battery model often used in the battery management system (BMS) to monitor and control lithium-ion batteries (LIBs). The accuracy and complexity of the ECM, hence, are very important. State of charge (SOC) and temperature are known to affect the parameters of the ECM and have been integrated into the model effectively. However, the effect of the state of health (SOH) on these parameters has not been widely investigated. Without a good understanding of the effect of SOH on ECM parameters, parameter identification would have to be done manually through calibration, which is inefficient. In this work, experiments were performed to investigate the effect of SOH on Thevenin ECM parameters, in addition to the effect of SOC and temperature. The results indicated that with decreasing SOH, the ohmic resistance and the polarization resistance increase while the polarization capacitance decreases. An empirical model was also proposed to represent the effect of SOH, SOC, and temperature on the ECM parameters. The model was then validated experimentally, yielding good results, and found to improve the accuracy of the Thevenin model significantly. With low complexity and high accuracy, this model can be easily integrated into real-world BMS applications.

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.

A simplification of the time-domain equivalent circuit model for lithium-ion batteries based on low-frequency electrochemical impedance spectra

The traditional time-domain equivalent circuit model (ECM) for Li-ion batteries may achieve high accuracy by identifying model parameters through limited dynamic conditions. However, the traditional ECM (TECM) parameter matching techniques based on time-domain may have the problem of adaptability of working conditions. To solve the problem of dependence on time-domain working conditions and improve the stability of the full-cycle modeling of lithium batteries, it is critical to establish the ECM based on the principle of electrochemical impedance spectroscopy (EIS). However, the full-frequency domain ECM structures (FECM) and the corresponding parameters based on the whole frequency ranges of the EIS employ too many resources for on-line estimation. In this paper, we firstly analyze the frequency region of the standard operating conditions of electric vehicles and theoretically discuss the rationality of the Simplified ECM base on the low-frequency region of the EIS. The proposed low-frequency domain ECM (LECM) simplifies the elements that describe the medium-high frequency regions of the EIS. It only uses the low-frequency region of the EIS to identify the model parameters. The results show that the accuracy of the proposed LECM is almost the same as that of FECM, and saves an average of 40% of the calculation load.

Effect of integrating the hysteresis component to the equivalent circuit model of Lithium-ion battery for dynamic and non-dynamic applications

Abstract The demand for lithium-ion (Li-ion) batteries is on the rise because of the increase in usage of electric vehicles (EVs) and other electrified applications. The battery management system (BMS) plays an important role in ensuring the safe and reliable operation of the battery. In order for the BMS to function and manage the battery pack effectively, a battery model is needed to monitor and predict the behavior of the battery. The equivalent circuit model (ECM) is widely used in online battery applications such as EVs, due to its simplicity and accuracy. There has been evidence suggesting that the addition of the hysteresis effect to the ECM would improve its accuracy. This paper presents an investigation into the effect of integrating hysteresis into the ECM, for both non-dynamic and dynamic applications. Two models are introduced, the first-order ECM and the first-order ECM with hysteresis (ECMwH). The model parameters are estimated using the Levenberg–Marquardt algorithm and training datasets. The models are then compared in terms of accuracy and computing time, using two driving cycles and a characterization cycle. The results show that the addition of the hysteresis effect to the first-order ECM improves the accuracy of the model in non-dynamic applications more significantly than in dynamic applications. The computing time increases, as expected, for the ECMwH, suggesting that it might not be beneficial to integrate hysteresis to battery models for online applications such as EVs.

Design of multi-stage charging power supply for TETS lithium battery based on PNGV model

In this paper, a multi-stage TETS charging system of the PNGV model of lithium-ion battery is proposed based on on the analysis of the equivalent circuit model of lithium-ion battery and the existing charging method. Using this system, the charging speed is increasing while the polarization and the temperature rising is suppressed. Taking into account the charging quality of the the lithium-ion battery, the actual charging curve is closer to the optimal charging curve in this system. Combining MATLAB and SIMPLORERMAXWELL multi-platform, the effectiveness of the scheme is verified by joint simulation. The simulation results have theoretical research and practical application value for the establishment of TETS charging system platform for lithium-ion battery.

State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter

Accurate estimation of the battery state of charge (SOC) is of great significance for enhancing its service life and safety. In this study, based on the fractional-order equivalent circuit model of lithium-ion battery, the SOC estimation methods using dual Kalman filter (DKF) and dual extended Kalman filter (DEKF) are simulated and compared, in terms of model accuracy and SOC estimation accuracy. Then, combining the advantages of the DKF and DEKF algorithms, an SOC estimation algorithm based on adaptive double Kalman filter is proposed. This algorithm uses the recursive least squares (RLS) method to update the battery model parameters online in real time, and employs the DKF algorithm to filter the SOC twice to reduce the interferences from the battery model error and the current measurement error. In the experimental studies, the measured SOC values are compared with the estimated SOC values produced by the proposed algorithm. The comparison results show that SOC estimation error of the proposed algorithm is within the range of ±0.01 under most test conditions, and it can automatically correct SOC to true value in the presence of system errors. Thus, the validity, accuracy, robustness and adaptability of the proposed algorithm under different operation conditions are verified.

Lithium-ion Battery Modeling and State of Charge Estimation

State of charge (SOC) is an important indicator for guiding the charging-discharging operation of lithium-ion batteries. In this article, the equivalent circuit model of lithium-ion battery and the variable forgetting factor (VFF) least squares model identification method are proposed. This parameter identification method can improve the accuracy of the lithium-ion battery model, thereby ensuring the accuracy of the SOC estimation. Furthermore, based on the lithium-ion battery model, the adaptive unscented Kalman filter (AUKF) algorithm is proposed to estimate SOC of lithium-ion batteries. Experimental results show that the AUKF algorithm is good robustness, fast convergence, practicality and small error in SOC estimation of lithium-ion batteries. In conclusion, the VFF least squares model identification method and the AUKF algorithm are promising engineering application method.

A Simplified Fractional Order Equivalent Circuit Model and Adaptive Online Parameter Identification Method for Lithium-Ion Batteries

In order to improve the battery management system performance and enhance the adaptability of the system, a fractional order equivalent circuit model of lithium-ion battery based on electrochemical test was established. The parameters of the fractional order equivalent circuit model are identified by the least squares parameter identification method. The least squares parameter identification method needs to rely on the harsh test conditions of the laboratory, and the parameter identification result is static; it cannot adapt to the characteristics of the lithium battery under dynamic conditions. Taking into account the dynamic changes of lithium batteries, a parameter adaptive online estimation algorithm for fractional equivalent circuit model is proposed. Based on the theory of fractional order calculus and indirect Lyapunov method, the stability and convergence of the estimator are analyzed. Finally, simulation experiments show that this method can continuously estimate the parameters of the fractional order equivalent circuit under UDDS conditions.

A physics-based distributed-parameter equivalent circuit model for lithium-ion batteries

A physics-based equivalent circuit model (ECM) is derived by applying finite volume method to a pseudo-two-dimensional (P2D) model of lithium-ion (Li-ion) batteries. Only standard passive components are used to construct the equivalent circuit, which reflects the fact that a Li-ion battery is an energy storage device. Voltages across and currents through the circuit elements in the ECM are identified with the respective internal electrochemical processes in the battery, thus allowing the parametric values of circuit elements to be expressed as functions of the Li-ion concentrations and temperature. Variations in the parametric values across the thickness of the battery leads to a distributed-parameter ECM amenable for wide range of applications. Furthermore, in contrast to existing reduced-order models of Li-ion battery which are described by differential algebraic equations, the ECM is governed by ordinary different equations wherein all the circuit components are expressed as explicit functions of the state and input variables. Hence, the developed model allows solution to be found directly using matrix algebra, resulting in rapid simulation study suitable for the development of computationally-efficient real-time battery control algorithm. Results of simulation based on the developed distributed-parameter ECM show close agreement with those obtained from a partial differential equation based P2D model under wide range of applied current rate, but at a much reduced computational burden.

Lithium-ion battery modeling and parameter identification based on fractional theory

To effectively use and manage lithium-ion batteries and accurately estimate battery states such as state of charge and state of health, battery models with good robustness, accuracy and low-complexity need to be established. So the models can be embedded in microprocessors and provide accurate results in real-time. Firstly, this paper analyzes the electrochemical impedance spectrogram of lithium-ion battery, and adopts impedance elements with fractional order characteristics such as constant phase element and Warburg element to improve the second-order RC integer equivalent circuit model based on the fractional calculus theory. Secondly, a fractional-order equivalent circuit model of lithium-ion battery is established, which can accurately describe the electrochemical processes such as charge transfer reaction, double-layer effect, mass transfer and diffusion of lithium-ion battery. Thirdly, based on the mixed-swarm-based cooperative particle swarm optimization, parameter identification of the fractional-order equivalent circuit model is conducted using the federal city driving schedule experimental data in the time domain. The simulation results show that the model has higher accuracy and better robustness against different driving conditions, different SOC ranges and different temperatures than the second-order RC equivalent circuit model. The SOC estimation accuracy based on the fractional-order equivalent circuit model of lithium-ion battery is validated.

A lithium ion battery model considering state-of-charge and battery current

In this paper, an electric circuit model for lithium-ion batteries is proposed for predicting the over-voltage transients after discharging or charging. Primary factors, such as state-of-charge (SOC), and battery current are separately experimented to examine their impacts. Kalman filter algorithm is applied to analyze the long-time recorded data, so as to identify the over-potential features during each different SOC stage. On monitoring battery current and voltage, the model is capable of predicting the over-voltage dynamics. Finally, experiments are carried out to verify the model to test the feasibility of the battery model.

An SOC estimation approach based on adaptive sliding mode observer and fractional order equivalent circuit model for lithium-ion batteries

A state of charge (SOC) estimation approach based on an adaptive sliding mode observer (SMO) and a fractional order equivalent circuit model (FOECM) for lithium-ion batteries is proposed in this paper. In order to design the adaptive sliding mode observer (SMO) for the SOC estimation, the state equations based on a FOECM of battery are derived. A new self-adjusting strategy for the observer gains is presented to adjust the observer in the estimating process, which helps to reduce chattering and convergence time. Furthermore, a continuous and smooth function called hyperbolic tangent function is applied to balance the chattering affection and the disturbance. At last, a battery simulation model is established to test the SOC estimation performance of the designed SMOs, and the results show the proposed approach is feasible and effective.

Identification of the Parameters in Equivalent Circuit Model of Lithium-Ion Battery

Nowadays, rechargeable lithium-ion batteries (LIB) have been commonly used in vehicles and mobile devices. A major environmental issue that concerns the use of lithium-ion battery is how to extend the life cycle of an aged or malfunctioned cell. One possible solution is to examine the response of the individual parts of an LIB and replace only those parts which fail to function well.Electrochemical Impedance Spectroscopy (EIS) is one of the most popular and convenient methods for battery examination, since it provides us with the general information about cell resistance. A typical impedance spectrum of the lithium-ion cell is composed of two partially overlapped semicircles and a straight line at low frequency end. However, these two semicircles, represented by the two RC circuits which correspond to SEI film and the combined effect of diffusivity, charge transfer, and double layer, are difficult to discriminate.This study adopted a simple EIS model of LIBs, whose equivalent circuit is shown in Fig. 1 [1]. In this case, each component delineates and models its corresponding physics. We swept the cell over the frequency range from 10 kHz to 0.01 Hz at various states of charge (SOCs). According to the previous works [2, 3] and our proposed fitting procedure, we could precisely fit the experimental spectra by the EIS model, as shown in Fig. 2. The determination of the nine parameters in this model enables us to further simulate the discharge curve, as shown in Fig. 3, which proves to be compatible with that obtained from the experiment [4].To separate two partially overlapped semicircles, it is necessary to find a method to distinguish Rct from Rsei . The charge transfer resistance Rct can be determined from the expression i 0=RT/nFRct , where the exchange current density i0 is evaluated by the electrochemical model simulation, and R and T respectively denote the gas constant and the Kelvin temperature. As soon as Rct is achieved, the curve fitting of the impedance spectrum helps us to obtain the other eight parameters. Further study will be conducted to find the relation between the nine parameters and SOC from the impedance spectrum. This relation is useful for electrochemical model simulation of lithium-ion batteries in the future.

Identification of dynamic model parameters for lithium-ion batteries used in hybrid electric vehicles

This paper presents an electrical equivalent circuit model for lithium-ion batteries used for hybrid electric vehicles (HEV). The model has two RC networks characterizing battery activation and concentration polarization process. The parameters of the model are identified using combined experimental and Extended Kalman Filter (EKF) recursive methods. The open-circuit voltage and ohmic resistance of the battery are directly measured and calculated from experimental measurements, respectively. The rest of the coupled dynamic parameters, i.e. the RC network parameters, are estimated using the EKF method. Experimental and simulation results are presented to demonstrate the efficacy of the proposed circuit model and parameter identification techniques for simulating battery dynamics.