Equivalent Circuit Model Parameters Research Articles

Optimal Charging Current Protocol with Multi-Stage Constant Current Using Dandelion Optimizer for Time-Domain Modeled Lithium-Ion Batteries

This study utilized a multi-stage constant current (MSCC) charge protocol to identify the optimal current pattern (OCP) for effectively charging lithium-ion batteries (LiBs) using a Dandelion optimizer (DO). A Thevenin equivalent circuit model (ECM) was implemented to simulate an actual LiB with the ECM parameters estimated from the offline time response data obtained through a hybrid pulse power characterization (HPPC) test. For the first time, DO was applied to metaheuristic optimization algorithms (MOAs) to determine the OCP within the MSCC protocol. A composite objective function that incorporates both charging time and charging temperature was constructed to facilitate the use of DO in obtaining the OCP. To verify the performance of the proposed method, various algorithms, including the constant current-constant voltage (CC-CV) technique, formula method (FM), particle swarm optimization (PSO), war strategy optimization (WSO), jellyfish search algorithm (JSA), grey wolf optimization (GWO), beluga whale optimization (BWO), levy flight distribution algorithm (LFDA), and African gorilla troops optimizer (AGTO), were introduced. Based on the OCP extracted from the simulations using these MOAs for the specified ECM model, a charging experiment was conducted on the Panasonic NCR18650PF LiB to evaluate the charging performance in terms of charging time, temperature, and efficiency. The results demonstrate that the proposed DO technique offers superior charging performance compared to other charging methods.

Fault Diagnosis of Lithium-Ion Batteries Based on the Historical Trajectory of Remaining Discharge Capacity

In recent years, the number of safety accidents in new-energy electric vehicles due to lithium-ion battery failures has been increasing, and the lithium-ion battery fault diagnosis technology is particularly important to ensure the safe operation of electric vehicles. This paper proposes a method for lithium-ion battery fault diagnosis based on the historical trajectory of lithium-ion battery remaining discharge capacity in medium and long time scales. The method first utilizes the sparrow search algorithm (SSA) to identify the parameters of the second-order equivalent circuit model of the lithium-ion battery, and then estimates the state of charge (SOC) of the lithium-ion battery using the extended Kalman filter (EKF). The remaining discharge capacity is estimated according to the SOC, and finally the feature vectors are used to diagnose the faults using box plots on the medium and long time scales. Experimental results verify that the root mean squared error (RSME) and mean absolute error (MAE) of the proposed SOC estimation method are 0.0049 and 0.0034, respectively. This method can accurately identify the faulty single cell in a battery pack with low-capacity single cells and promptly detect any abnormalities in the single cell when a micro-short circuit fault occurs.

A Comparison of Battery Equivalent Circuit Model Parameter Extraction Approaches Based on Electrochemical Impedance Spectroscopy

This paper presents three approaches to estimating the battery parameters of the electrical equivalent circuit model (ECM) based on electrochemical impedance spectroscopy (EIS); these approaches are referred to as (a) least squares (LS), (b) exhaustive search (ES), and (c) nonlinear least squares (NLS). The ES approach is assisted by the LS method for the rough determination of the lower and upper bound of the ECM parameters, and the NLS approach is incorporated with the Monte Carlo run such that different initial guesses can be assigned to improve the goodness of EIS fitting. The proposed approaches are validated using both simulated and real EIS data. Compared to the LS approach, the ES and NLS approaches show better fitting accuracy at various noise levels, whereas in both the validation using simulated EIS data and actual EIS data collected from LG 18650 and Molicel 21700 batteries, the NLS approach shows better fitting accuracy than that of LS and ES approaches. In all cases, compared with the ES approach, the computational time of the NLS approach is significantly faster, and compared with the LS approach, the NLS approach shows a minimal difference in computational time and considerably better fitting performance.

Advanced parameter estimation for lithium-ion battery model using the information sharing group teaching optimization algorithm

Accurate battery modeling is crucial for optimizing the performance and safety of Lithium-ion batteries (LiBs), particularly in applications such as electric vehicles and smart grids. This paper introduces the Information Sharing Group Teaching Optimization Algorithm (ISGTOA), a novel human-based metaheuristic algorithm designed to estimate the 21 parameters of third-order Equivalent Circuit Model (ECM) for LiBs. Unlike existing methods, ISGTOA effectively manages the increased complexity of a model through advanced group teaching strategies and sophisticated information-sharing mechanisms inspired by classroom dynamics. We validated the effectiveness of ISGTOA using two distinct datasets—High Dynamic Profile (HDP) and Urban Dynamometer Driving Schedule (UDDS)—across various LiB chemistries (NCA and NMC) and temperature conditions (−5 °C, 25 °C and 45 °C). The results demonstrate that ISGTOA achieves superior parameter estimation accuracy and convergence speed compared to established and recent optimization methods such as TLBO, TLSBO, AISA, MTBO, and DTBO. Specifically, ISGTOA attained a minimum RMSE of 8.357 mV with rapid convergence and high stability in the HDP dataset and minimized RMSE to 10 mV within ten iterations at both 25 °C and 45 °C in the UDDS dataset. Additionally, ISGTOA exhibited high efficiency (up to 97.75 %) under varying thermal environments. This work not only introduces a novel algorithm for complex battery modeling but also sets the stage for future advancements in real-time battery management systems, emphasizing the importance of robust, versatile, and efficient parameter estimation techniques.

State of Charge Estimation for Lithium-Ion Batteries Using Optimized Model Based on Optimal HPPC Conditions Created Using Taguchi Method and Multi-Objective Optimization

This study proposes a comprehensive methodology for accurate State of Charge (SOC) estimation in lithium-ion batteries by optimizing equivalent circuit model (ECM) parameters under varying temperature conditions using the Taguchi method. Analysis of Variance (ANOVA) was employed to evaluate the influence of these parameters on ECM accuracy. Experiments were conducted at −10 °C, 25 °C, and 40 °C to evaluate the effects of pulse time gap, discharge pulse time, and C-rate on SOC estimation accuracy. A genetic algorithm-based multi-objective optimization technique was employed to minimize RMSE in the extended Kalman filter (EKF) SOC estimation process. The results showed that temperature significantly impacts SOC prediction, with deviations most pronounced at low (−10 °C) and high (40 °C) temperatures. When assessments are conducted for different SOC levels (SOC90, SOC50, SOC30), the key results highlight the substantial influence of pulse time gap and discharge pulse time on model accuracy. Also, it was observed that there is a significant reduction in RMSE, indicating improved performance under optimized conditions. The findings are particularly relevant for real-time applications, such as electric vehicles, where accurate SOC estimation is crucial for battery management.

State-of-health estimation of lithium-ion batteries using multiple correlation analysis-based feature screening and optimizing echo state networks with the weighted mean of vectors

Lithium-ion batteries (LIBs) are widely employed in electric vehicles (EVs) and energy storage systems owing to their high energy density, low self-discharge rate, and superior longevity. As a vital evaluation index for the degradation state of LIBs, the state of health (SOH) must be accurately estimated. This study adopts an electrochemical impedance spectroscopy (EIS)-based equivalent circuit model (ECM) to estimate battery SOH. The internal dynamic electrical behaviors of LIBs are decoupled by the distribution of relaxation times (DRT) method, whereby the critical degradation features are extracted from the DRT curves and the fitted ECM parameters. Subsequently, referring to the ensemble learning approach (ELA), the multiple correlation analysis (MCA) is utilized to identify the most pertinent degradation features. The battery data are subjected to a comprehensive analysis with five types of correlations to ascertain the optimal number and combination of health indicators (HIs). Furthermore, the weighted mean of vectors (INFO) algorithm is employed to optimize the hyperparameters in the echo state network (ESN) model for SOH estimation. The echo state networks model optimized with the weighted mean of vectors algorithm (INFO-ESN) is verified with eight types of LIBs under different operating conditions. Experimental results of the proposed method manifest that the root mean square error (RMSE) and mean absolute error (MAE) of the battery SOH range from 0.32 % to 1.06 %, thereby verifying the accuracy and robustness of the proposed method.

A Quantum Particle Swarm Optimization Extended Kalman Quantum Particle Filter approach on state of charge estimation for lithium-ion battery

The accurate estimation of battery state of charge serves as the foundation for estimating state of health, remaining useful life, and safety, making it an indispensable part of battery management system. Based on the lithium-ion battery parameter identification using quantum particle swarm optimization, this paper presents a state of charge estimation method utilizing the Extended Kalman Quantum Particle Filter. A Quantum Particle Swarm Optimization algorithm is used for second-order equivalent circuit model parameter identification. By combining Extended Kalman Filter with Particle Filter and employing Grover search algorithm for resampling of quantized particles, the Extended Kalman Quantum Particle Filter is designed for estimation. Validation is conducted under standard operating conditions, and the Quantum Particle Swarm Optimization Extended Kalman Quantum Particle Filter algorithm demonstrates better accuracy and adaptability compared to Extended Kalman Filter, Extended Kalman Particle Filter and other popular algorithms under FUDS, UDDS and DST working conditions by two types of battery. Both theoretical and experimental results indicate good performance of Quantum Particle Swarm Optimization Extended Kalman Quantum Particle Filter in state of charge estimation.

Thermal Management of Lithium-Ion Battery Pack Using Equivalent Circuit Model

The design of an efficient thermal management system for a lithium-ion battery pack hinges on a deep understanding of the cells’ thermal behavior. This understanding can be gained through theoretical or experimental methods. While the theoretical study of the cells using electrochemical and numerical methods requires expensive computing facilities and time, the Equivalent Circuit Model (ECM) offers a more direct approach. However, upfront experimental cell characterization is needed to determine the ECM parameters. In this study, the behavior of a cell is characterized experimentally, and the results are used to build a second-order equivalent electrical circuit model of the cell. This model is then integrated with the cooling system of the battery pack for effective thermal management. The Equivalent Circuit Model estimates the internal heat generation inside the cell using instantaneous load current, terminal voltage, and temperature data. By extrapolating the heat generation data of a single cell, we can determine the heat generation of the cells in the pack. With the implementation of the ECM in the cooling system, the coolant flow rate can be adjusted to ensure the attainment of a safe operating cell temperature. Our study confirms that 14% of pumping power can be reduced when compared to the conventional constant flow rate cooling system, while still maintaining the temperature of the cells within safe limits.

Relating state-of-charge to impedance and equivalent circuit parameters in lithium-ion cells: An experimental study

The wide-band impedance of Lithium-ion (Li-ion) batteries has become a focal point for researchers interested in State-of-Charge (SOC) estimation and battery modeling. However, the interplay between SOC, wide-band impedance, and model parameters has not been extensively explored. This paper addresses this gap by investigating how SOC impacts the impedance and Equivalent Circuit Model (ECM) parameters of a Li-ion battery cell through empirical measurements. The study utilizes discharge tests to vary the SOC and employs the Coulomb Counting Method (CCM) to estimate the approximate SOC from the response signals. A novel measurement technique is introduced and applied to determine a cell’s wide-band impedance at different SOC levels. This innovative approach uses a Pseudo-random Impulse Sequence (PRIS) perturbation signal to measure wide-band cell impedance. The collected impedance data is then used to estimate the ECM parameters. Experimental findings reveal an inverse relationship between impedance and SOC. Additionally, the ECM parameters exhibit significant correlation with SOC, particularly in mid- to low-frequency regions. This research highlights that SOC profoundly influences ECM parameters, offering valuable insights into the performance of Li-ion batteries under various conditions.

Identification of the dynamic model of second-life lithium-ion cells through Subspace System Identification and similarity transformation

When lithium-ion batteries (LiBs) reach the end of their first useful life in electric vehicles (EVs), they can still be used in applications with lower power demands, a process known as second-life. However, to ensure that LiBs – or cells – removed from EVs operate safely, efficiently, and reliably in a second application, various tests and procedures must be applied to study their internal conditions. Some information about the conditions of the lithium-ion cells can be obtained from the parameters of its equivalent circuit model(ECM). However, the tests to obtain blackthe ECM parameters usually require taking the LiBs out of service and testing their cells in laboratory benches with special equipment, which is costly and time-consuming. Therefore, this work proposes a methodology to identify the ECM of lithium-ion cells based on Subspace System Identification (SSI) methods. This procedure can be executed online, while the LiBs are being used in the specified application. SSI methods have been widely adopted to identify the dynamic model of lithium-ion cells, but they return models without a physical meaning, called non-parametric models. This type of model cannot be used to address the internal conditions of a lithium cell, because its parameters do not have any physical meaning. To solve this problem, a novel method for estimating the lithium-ion cell physical parameters, in the ECM format, and from its non-parametric model, is proposed in this work. The procedure is based on similarity transformation techniques and special characteristics of the ECM. To validate the proposed method, nine samples of cells from the same manufacturer were studied. These cells had distinct degradation conditions and were removed from heavy-duty EVs at the end of their first life. The results showed that: (a) a good approximation between the identified model voltage output and the actual cells’ experimental voltage output was achieved, with root mean square error values as small as 2.26 mV; (b) it was possible to identify the ECM of the tested cells and their parameters using the proposed similarity transformation; and (c) the identified parameters can be used to detect the internal conditions of the cells.

Inverse design of dual-bandpass metasurface filters empowered by the multi-objective genetic algorithm

Multi-band metasurface filters are becoming increasingly pivotal in high-capacity communication technologies. Traditional methods for designing metasurface structures, to date, have relied on empirical approaches to obtain target electromagnetic responses, thereby suffering from low efficiency. Here, we demonstrate an advanced approach for the inverse design of a multi-band metasurface filter, which consists of a multi-objective genetic algorithm (MOGA) in tandem with equivalent circuit model (ECM) analysis. This integration converts specific frequency response requirements into ECM parameter constraints, significantly streamlining the metasurface design and optimization process and offering superior solutions. Using this inverse design method, we theoretically propose a dual-bandpass metasurface filter which can exhibit transmission passbands in any two adjacent frequency ranges among the X-, Ku-, and K-bands. Further, numerical simulations validate the performances of the proposed device, which show great agreement with MOGA-based predictions. Our results pave the way to the effective inverse design of multi-passband metasurface filters which are useful in many applications, such as microwave filters, radar and satellite communication systems, and radio frequency identification devices.

A novel least squares support vector machine-particle filter algorithm to estimate the state of energy of lithium-ion battery under a wide temperature range

The state of energy (SOE) is a key indicator for lithium-ion battery management systems (BMS). Based on the second-order resistance-capacitance equivalent circuit model and online parameter identification using the dynamic weights particle swarm optimization (DWPSO) method, a least-squares support vector machine-particle filter (LSSVM-PF) algorithm is proposed to construct a particle filter to estimate the SOE of a lithium-ion battery, and then transfer the resulting estimation error together with the experimentally measured voltage and current values to a trained LSSVM model, and use the LSSVM model to optimize the SOE estimates obtained by the PF algorithm twice to improve the accuracy of SOE estimation for lithium-ion batteries. The feasibility of the proposed algorithm is verified using two complex operating conditions and at three different temperatures. The validation results show that the maximum error of SOE estimation of the proposed algorithm is 0.0284 for a wide temperature range under Beijing Bus Dynamic Stress Test (BBDST) condition, and 0.0226 for a wide temperature range under Dynamic Stress Test (DST) condition. The proposed algorithm significantly improves the accuracy of SOE estimation and provides a reference for fundamental applications of lithium-ion batteries.

Robust equivalent circuit model parameters identification scheme for State of Charge (SOC) estimation based on maximum correntropy criterion

Equivalent circuit model (ECM) parameters identification, which aims to identify the model parameters of ECM accurately is vital for assessing battery status and refining battery management systems (BMS), extensive research has been conducted in this field. However, most of the existing studies rely on global similarity criteria such as Root Mean Square Error (RMSE) and Sum of Squares due to Error (SSE), which are highly sensitive to non-Gaussian noise, so they may not perform effectively when faced with the non-Gaussian noise which is often encountered in battery working environments. This article presents a robust ECM parameter identification scheme termed the Maximum Correntropy Criterion-based Gradient Ascending scheme (MCCGA). The proposed MCCGA scheme adopts correntropy for similarity assessment and leverages a gradient ascent algorithm to optimize the model parameters iteratively. Through these methods, the MCCGA scheme not only identifies model parameters with precision but also remains robustness to non-Gaussian noise. Extensive experimental results based on public dataset are provided, which validate the effectiveness, robustness and convergence of the proposed MCCGA scheme.

Electrical Equivalent Circuit Model and RC Parameter Estimation for Vanadium Redox Flow Battery by Considering Self-discharge

Electrical Equivalent Circuit Model and RC Parameter Estimation for Vanadium Redox Flow Battery by Considering Self-discharge

Online state of health estimation of lithium-ion batteries through subspace system identification methods

When Lithium-ion Batteries (LiBs) reach the end of their first life in electric vehicles (EVs), they can still be used in applications with lower power demands, a process known as second-life. However, to ensure that LiBs – or cells – removed from EVs operate safely, efficiently and reliably in a second application, several tests and procedures must be applied to study their internal conditions. Naturally, one of the most important parameters to be determined is the state of health (SoH). However, the available processes for determining the SoH of lithium-ion cells are limited by high costs, relatively long test times and the need for specific equipment, limiting the second-life market. Hence, this work proposes a methodology to estimate the SoH of lithium-ion cells, based on subspace system identification (SSI) methods, where the parameters estimated for the equivalent circuit model (ECM) of a given cell are associated with its SoH. To validate the proposed methodology, nine cell samples from the same manufacturer were considered, which were removed from heavy-duty EVs at the end of their first life. The obtained results showed that: (a) good approximations between the identified models and the actual cells were achieved, with root mean square error (RMSE) values as small as 1.32 mV; (b) SSI methods can be applied online, while the LiBs are still operating in the EV during their first life, eliminating the need of additional tests; and (c) there is a clear association between ECM parameters and the SoH, so it was possible to estimate the SoH of the samples with RMSE values varying from 2.11% to 3.34%. Therefore, the proposed methodology offers significant improvements when compared to the conventional capacity tests, including the possibility of estimating the SoH relatively fast, online and without the need for specific equipment.

Electrothermal modeling of lithium-ion batteries using an artificial intelligence technique-based approach for powerwall applications

The Powerwall, an innovative home battery powered by solar energy, is gaining popularity in the United States and Australia due to its ability to provide complete power to homes and serve as a backup during electrical supply interruptions. Recently, lithium-ion (Li-ion) battery technology has received significant attention from the industry and academia, standing out for offering greater energy capacity, power density, efficiency, and lower self-discharge rate compared to other technologies such as NiCd and NiMH batteries. Initially, this research aimed to model the Li-ion cells of the Powerwall using the equivalent circuit model (ECM). However, a detailed review of the literature indicated that a data-based approach, employing Deep Learning (DL) techniques or deep neural networks, represents the state of the art in the field. DL, a subset of machine learning and part of Artificial Intelligence (AI), offers notable advantages over ECM, including: i) high precision in estimating the non-linear relationships between voltage, current, temperature, and hidden variables such as the State of Charge (SOC); ii) the ability of a single artificial neural network to model the behavior of a Li-ion cell across different temperature ranges (example: from 0°C to 40°C); and iii) overcoming the challenge of identifying ECM parameters. Therefore, with the advancement of the research, the objective was updated to investigate and develop DL models, specifically feed-forward neural networks, for estimating the SOC of lithium-ion batteries in Powerwalls. The results obtained focus on the precise estimation of the SOC of Li-ion cells, underlining the efficacy and innovation of this methodological approach.

Diagnosis of PEM Fuel Cell System Based on Electrochemical Impedance Spectroscopy and Deep Learning Method

In this paper, a new fault diagnosis framework for proton exchange membrane fuel cells based on Electrochemical Impedance Spectroscopy (EIS) and the deep learning method is proposed. Specifically, this work employs the PEMFC knowledge to drive the training process of the deep learning network, which makes it possible to improve fault diagnosis performance by deep learning algorithms with a limited scale of actual measured EIS data. A pre-training network is developed to predict the equivalent circuit model (ECM) parameters, which could reduce the time consumption of ECM parameter identification. Besides, considering that the ECM parameters are susceptible to significant changes due to non-fault operation, a fine-tuning network is designed to generate robust diagnosis features, which could support the proposed framework working in different environments. Moreover, the complex neural networks are adopted in the proposed framework to extract features from EIS data, which is composed of complex impedances. Finally, a new evaluation metric PScore is proposed to assess the performance of the diagnosis framework from the perspective of practical applications. The experiments are performed to demonstrate the effectiveness of each component in the framework, and the proposed algorithm has significant improvements in fault diagnosis performance and computational efficiency over traditional algorithms.

Optimization of the SOC-based multi-stage constant current charging strategy using coyote optimization algorithm

This study presents a new strategy which optimizes the multi-stage constant current (MSCC) charging algorithm with state-of-charge (SOC)-based transition conditions (MSCCSOC) by searching for the optimal values of transition state-of-charge (SOC) and charging currents using the coyote optimization algorithm (COA). The paper firstly uses the electrochemical impedance spectroscopy (EIS) analysis to construct the equivalent circuit model (ECM) of the lithium-ion battery, and particle swarm optimization (PSO) is utilized to determine the parameters of the battery ECM within each 1 % SOC. The study employs the COA for the first time to tackle the challenging multi-objective MSCC optimization problem, which involves nine parameters. By not relying on multiple charging experiments and not restricting the search range of SOC transition and charging current values, the proposed approach can identify the global optimal solution, thus being advantageous over existing methods. The proposed method considers both shortening the charging time and reducing the charging losses. The experimental results show that compared with the traditional 1C CC-CV charging method, the proposed strategy can improve the average temperature rise, charging time, and maximum temperature rise by 17.6 %, 34.0 %, and 26.0 %, respectively. Furthermore, the proposed method outperforms other state-of-the-art MSCC charging algorithms and optimization techniques with limited searching range. Therefore, the proposed strategy provides a promising solution for obtaining the optimal setting for MSCCSOC, which can lead to reduced charging time and charging losses, thereby improving the battery's performance and lifespan.

Parameter estimation of ECM model for Li-Ion battery using the weighted mean of vectors algorithm

Accurate parameter estimation of the equivalent circuit model (ECM) for Li-Ion batteries (LiBs) allows for better behavior modeling and understanding. This is crucial for various applications, such as battery management systems (BMSs) and renewable energy systems, as it enables more precise performance prediction and optimization. This article introduces a novel artificial intelligence (AI) approach to estimate the ECM parameters of LiBs. The proposed method leverages the innovative weIghted meaN oF vectOrs (INFO) algorithm to optimize ECM parameter values. INFO combines multiple vectors, considering their relative importance, to generate a single vector. The algorithm minimizes the disparity between the ECM’s estimated voltage and the battery’s measured voltage. The effectiveness of the proposed method is assessed using a test profile based on real-world driving data. Furthermore, A comparative analysis is conducted with other state-of-the-art optimization algorithms, including Artificial Ecosystem Optimizer (AEO), Grey Wolf Optimizer (GWO), Artificial Hummingbird Algorithm (AHA), Harris Hawks Optimization (HHO), Leader Harris Hawks Optimization (LHHO), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Adolescent Identity Search Algorithm (AISA). Results demonstrate that the INFO outperforms these methods in terms of accuracy and convergence speed. The proposed INFO algorithm offers a promising approach for accurate parameter estimation in LIB modeling, contributing to improved BMS and enhanced performance prediction.

An Ameliorated Small-Signal Model Parameter Extraction Method for GaN HEMTs up to 110 GHz with Short-Test Structure

An improved method of extracting small-signal equivalent circuit model parameters for gallium nitride high electron mobility transistors (GaN HEMTs) is presented. This paper intends to present a method to extract the parasitic inductance and resistance of transistors based on the short-test structure without the open-circuit test structure. The parasitic capacitance of transistors is extracted by the method based on the size scalable model. Compared with the traditional COLD-FET method, the extraction procedure is simpler and more convenient. After removing the influence of parasitic elements, the intrinsic parameters of the model can be extracted by the S-parameters measured at different bias points. The experimental results show that the simulation results have good agreement with the measured results in the range of 0.5∼110 GHz.