Equivalent Circuit Model Parameters Research Articles

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.

Parameter extraction for photodiode equivalent circuit model based on hybrid genetic algorithm

Photodiode equivalent circuit models often involve numerous parameters, making the parameter extraction process complex. Therefore, this work presents a hybrid genetic algorithm (HGA) to extract photodiode parameters. Firstly, we deduce the calculation formula of the scattering parameters of the photodiode equivalent circuit model. Then, to address the limitations of the standard genetic algorithm (SGA) that its slow convergence and extended search times, we incorporate the elite strategy and acceleration operator, enhancing the local search ability of HGA. We compare the performance of the HGA with the other four optimization algorithms under multiple sets of measured data. Results show that HGA has better performance in parameter fitting, convergence speed, and accuracy from 10 MHz to 40 GHz, highlighting its superiority. The algorithm significantly simplifies photodiode parameter extraction, and provides a feasible solution for the parameter extraction of optoelectronic devices.

Variable recursive least square algorithm for online battery equivalent circuit model parameters identification for electric vehicles

Variable recursive least square algorithm for online battery equivalent circuit model parameters identification for electric vehicles

Cut‐set matrix methods for frequency response analysis curves of lumped parameter equivalent circuit model of three‐winding power transformer

SummaryTo accurately and efficiently calculate the frequency response of the lumped parameter equivalent circuit model (LPECM) of a transformer winding is the basis for studying the simulation method of the frequency response analysis (FRA). In this paper, two different cut‐set matrix (CSM) methods, including fundamental cut‐set (FCS) and independent cut‐set (ICS) matrix methods, are proposed to calculate the FRA curves of the LPECM of a three‐winding power transformer. First, based on graph theory and electrical circuit laws, the basic CSM equation is deduced. Second, four different FCS matrix selection methods of the LPECM are introduced and the best FCS matrix is determined by deeply analyzing their characteristics. Then, an ICS matrix method is proposed to obtain the ICS of the LPECM. Furthermore, FCS and ICS are taken into the CSM equation to calculate the FRA results of the LPECM, respectively. Finally, the accuracy of the proposed methods is validated by Multisim software and the performance of these two methods is compared with node voltage matrix (NVM) method by analyzing the calculation time. The results show that FCS and ICS matrix methods both can be used to accurately obtain the FRA results of the LPECM of the three‐winding power transformer, but ICS is more simple than FCS matrix method due to avoiding the procedure for the selection of the tree. In addition, since ICS matrix method has the shortest running time among these methods, it can be used to improve the calculation efficiency of the FRA curves of the LPECM of a three‐winding power transformer.

A comparative evaluation of equivalent circuit and finite element electrical skin modelling techniques

Mathematical models are essential to our understanding of the electrical properties of the skin. In this paper, two types of simulation model, an equivalent circuit and a finite element simulation were investigated and compared to evaluate their accuracy. Impedance spectra were measured, between 100 Hz and 50 MHz, (the limits of the available spectrum analyser) of a pair of electrodes placed on skin and these spectra used to find the parameters of a standard equivalent circuit model. The resulting indicated that the components of the equivalent circuit may represent different parts of the skin physiology that indicated by the literature. A simulation model was constructed in COMSOL, with the dimensions, permittivity and conductivity of each skin layer taken from across the published literature. This model was tested for sensitivity to the thicknesses of tissue layers as well as the shape of the boundary between layers. It was found that changing the layer thicknesses only had a significant effect for the stratum corneum and dermis, and that changing the shape of the boundary between layers created an impedance change of up to two times at certain higher frequencies (>1 kHz). While the impedance curves generated by the two models had the same overall profile, there was a difference of up to 100 times in their DC impedance values. This indicated that the broad understanding of how electrical signals of different frequencies pass through the skin is correct, but that significant insufficiencies exist in the published properties of the skin layers, particularly the stratum corneum and that finding more accurate values for these properties is necessary for the development of better models.

Accurate Electromagnetic Force Analysis of Offshore Wind Power Transformer Windings Based on Fractional Order Lumped Parameter Model

Accurate calculation of the electromagnetic force distribution of transformer windings under different loads and fault conditions is of great significance for transformer maintenance, condition evaluation and life prediction. Due to the influence of offshore wind power systems, offshore wind power transformers have high harmonic content and large changes in load rates, which can easily cause the coil destabilization, winding deformation or even damage because of the uneven distribution of the electromagnetic force. To improve the accuracy of electromagnetic force calculation, this paper proposes a fractional order numerical method. First, a three-dimensional axisymmetric transformer model and a symmetrical lumped parameter equivalent circuit model are established, respectively, based on field-circuit coupling. Second, the fractional order approximation of circuit components is realized by using the improved Oustaloup filter. In the fractional order model, the transformer is replaced by the lumped parameter equivalent circuit model. Third, as in the calculation process for integer order electromagnetic force, the integer order current has a large error, and the current waveform does not match the actual power frequency. The fractional order current and electromagnetic force at the 0.9 order are closer to the rated value. Finally, the effects of different load rates, three-phase short circuits and harmonic conditions are studied with the fractional order model. Compared with the traditional integer order finite element electromagnetic model, the fractional order equivalent circuit model established in this paper is more accurate and suitable for electromagnetic force calculation. The proposed method is significant for the structural design and state detection of transformers and also could be applied in the analysis of other dry-type transformers.

State of health estimation method for lithium-ion batteries based on multiple dynamic operating conditions

Lithium-ion battery state of health estimation is an important task for electric vehicles. However, the uncertainty and complexity of operating conditions pose significant challenges for state of health estimation. In this paper, a state of health estimation method with dynamic operating conditions generalization is developed. The equivalent circuit model parameters are kept unchanged, and the voltage is predicted based on the equivalent circuit model of initial aging point. The integral voltage error is extracted as an indicator of battery aging, and feature fusion is achieved by combining the feature of dynamic operating conditions. By cross-validation under dynamic operating conditions, the fused features are input into a back propagation neural network to achieve accurate estimation of state of health. At the same time, the voltage error reference baseline and pseudo-state of charge interval that affect the accuracy of the model estimation are discussed. After selecting the appropriate voltage error reference baseline and pseudo-state of charge interval, the mean absolute errors of the state of health estimation obtained on the dynamic operating conditions are all around 1%. The proposed state of health estimation method has low computational requirements, eliminates the dependence on the accuracy of state of charge , and can achieve generalization of multiple dynamic operating conditions, making it potentially applicable in actual vehicle applications.

1D convolutional neural network combined with long-short term memory-based cell-to-cell inconsistency estimation considering recursive least squares and Euclidean distance

As the scale of application utilizing batteries as a power source expands, operation at the cell-tray and pack level has become indispensable. Such expansion amplifies the importance of accurate and consistent monitoring of cell-to-cell inconsistencies during battery operation for efficient and safe use. Consequently, this study addresses the limitations associated with inconsistency evaluations that rely solely on voltage deviation, which may lead to inaccurate inconsistent information, contingent on operational conditions and assessment timelines. By integrating the internal dynamics of an RLS-based 24S1P cell-tray, the aim is to derive deviations in electrical equivalent circuit model (EECM) parameters between cells, facilitating real-time battery inconsistency evaluations. The extracted EECM parameters are quantified utilizing the Euclidean distance for an effective quantification and scoring of multi-variables for inconsistency assessment. Additionally, to alleviate the computational burden associated with deriving the inconsistency evaluation index, an approach has been adopted that learns 60 % of the data prior to the occurrence of inconsistency through model-based index training, thereby verifying the results of the inconsistency estimation. In this process, a 1D CNN-LSTM model is developed, capable of proficiently learning and estimating the patterns of data changes. Finally, by benchmarking performance against traditional imbalance evaluations based solely on voltage deviation, this study demonstrates the robustness and precision of the proposed methodology, underscoring its capability for accurate imbalance evaluation, irrespective of SOC segment or evaluation timing.

State of charge estimation and error analysis of lithium-ion batteries for electric vehicles using Kalman filter and deep neural network

The lithium-ion battery has a great significance in meeting the growing demand for Electric Vehicles (EVs) due to its higher energy density, longer life cycle, and notable nominal voltage and capacity. One crucial parameter for lithium-ion batteries is the State of Charge (SOC), which represents the available capacity and ensures that the system operates in a secure and reliable mode for EVs. SOC plays a significant role in the Battery Management System (BMS). This research aims to propose an Equivalent Circuit Model (ECM) based on Kalman filtering method and a data-driven technique, Deep Feed-Forward Neural Network (DFNN), for accurate SOC estimation of Electric Vehicle Battery (EVB). Initially, lithium-ion battery parameters are identified using a second-order RC (2-RC) Equivalent Circuit Model (ECM). Subsequently, battery modeling is performed, and various operating conditions such as terminal voltage, load current, and temperature are measured to obtain initial values for the filtering method used in SOC estimation. These operating conditions are crucial for ensuring safe and efficient charging and discharging of lithium-ion batteries. Based on the identified ECM parameters, SOC estimation error and bound error are then minimized using Kalman Filter (KF), Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) techniques. These filtering methods are employed to accurately estimate the SOC of the battery. The results demonstrate that the proposed model based on KF and EKF algorithms estimates SOC bound error within 2.5 % - –2 % and estimation error <1.5 % - –0.7 %. On the other hand, the UKF estimates a SOC bound error of 1.5 % and an estimation error of 0.5 %, proving the algorithm's efficiency and reliability. Particularly, this estimation error rejects measurement noise and parametric uncertainties for lithium-ion batteries to drive EVs with efficacy using UKF. Hence, the UKF algorithm estimated SOC has low estimation error, ensuring more accurate results. Finally, data-driven, DFNN method is implemented for accuracy enhancement of SOC estimation with trained 20 iterations and epochs data. Using this method, the SOC estimation accuracy is satisfactory with only 0.04 % Root Mean Squared Error (RMSE). The validation results indicate that the model-based filtering method is an effective method for SOC estimation to be applicable. In contrast, in a novel data-driven approach, SOC estimation accuracy is improved by approximately 0.46 %.

Thermal Equivalent Circuit Model and Parameter Estimation for High-Capacity Li-Ion Cell

The equivalent circuit model (ECM) has gained popularity as a simplified and computationally efficient battery model. However, an appropriate model is required to accurately calculate terminal voltage, state of charge (SOC), and temperature for high-capacity Li-ion batteries used in hybrid electric and electric vehicles. In this study, we integrate the ECM with an energy balance model to calculate the cell temperature. Furthermore, we propose improved model structures and parameter estimation strategies to effectively characterize high-capacity batteries. First, the actual SOC is calculated considering the actual discharge capacity. Second, as the current increases, the overcalculated resistance is corrected. Finally, ECM parameters are estimated using experimental data and the genetic algorithm (GA). To facilitate the parameter-search process for GA, we employ the dimensionless scale-up method and the Pareto optimal concept. The thermal ECM is validated using experimental data from 57.6 Ah batteries, demonstrating voltage and temperature calculation errors of less than 1.71% and 3.51%, respectively.

State of charge estimation for the vanadium redox flow battery based on the Sage–Husa adaptive extended Kalman filter

SummaryFocusing on improving the accuracy of vanadium redox flow battery (VRFB) state of charge (SOC) estimation, this paper will combine the extended Kalman filter (EKF) estimator with the Sage–Husa adaptive method, referred to as the SAEKF estimator. Firstly, a second‐order Equivalent Circuit Model (ECM) is established to provide the correct parameterization and degrees of freedom. Next, under a hybrid pulse power characterization (HPPC) text, the parameter estimator in MATLAB/Simulink is utilized to identify the ECM parameters by using nonlinear least squares method with Trust‐Region‐Reflective (TRR) iterative algorithm. Then, during the HPPC test, the estimators implemented on the ARM‐Cortex STM32F103 estimate the VRFB SOC under both the 0°C and 5°C conditions. Finally, the mean absolute error (MAE) of the IEKF estimator are 4.66% at the 0°C and 0.895% at the 5°C. In the meantime, the MAE of the SAEKF estimator are 4.15% at the 0°C and 0.703% at the 5°C. The evaluation factors of the 0°C and 5°C experiments in the SAEKF estimator are smaller than those of the IEKF and EKF estimators, indicating that the SAEKF estimator outperforms the IEKF estimator in VRFB SOC estimation.