Traditional Equivalent Circuit Research Articles

Equivalent circuit for assessing pore size distribution in porous electrodes by EIS

The size, geometry and arrangement of pores can significantly affect both the activity of electrocatalysts and the performance of supercapacitors. Electrochemical impedance spectroscopy (EIS) is a powerful, non-invasive diagnostic tool for characterizing porous conductive media. To date, the impedance of porous electrodes characterized by the distribution of pore sizes has been described only on the basis of numerical models. Here, for the first time, the impedance of such systems is provided in the form of analytical solutions valid in high and low frequency range. The model enables traditional equivalent circuit fitting to impedance of electrodes characterized by log–normal distribution of pore sizes. The analytical expressions for the circuit elements give access to the electrode idealized geometry in terms of log-normal distribution. The model was applied for the analysis of the electrochemical impedance of activated carbon electrode in a sulphuric acid solution. The width of pore size distribution, mean pore radius, pore length and the number of pores can be determined from a single impedance spectrum.

Investigation of the equivalent circuit and performance of an ultrasonic transducer under a force load

In ultrasonic processing technology applications, the force load can cause a drift in the resonance frequency of the ultrasonic transducer and significantly reduce its mechanical quality factor. The traditional equivalent circuit of an ultrasonic transducer can only be used to calculate performance parameters without a force load but not with a force load. Based on Mason’s equivalent circuit, a new equivalent circuit for ultrasonic transducers under a force load is derived while considering the effects of the force load on the material parameters and various types of losses in piezoelectric ceramics. Furthermore, performance parameters are analyzed, such as the resonance frequency, effective electromechanical coupling coefficient, and mechanical quality factor. The ultrasonic transducer sample is produced and the experimental platform is constructed for applying force loads on the ultrasonic transducer. The theoretical model is verified by static loading on the ultrasonic transducer. The proposed equivalent circuit provides theoretical guidance for tracking the exact resonance frequency and performance parameters of force-loading ultrasonic transducers.

Adaptive Piecewise Equivalent Circuit Model With SOC/SOH Estimation Based on Extended Kalman Filter

Battery modelling plays a critical role in battery management tasks. A model that provides accurate estimations of state of charge and state of heath in varying operating conditions could significantly improve the performance of battery management systems. Departing from existing literature, this paper presents a self-adaptive Piecewise Equivalent Circuit Model (PECM) based on Extended Kalman Filter (EKF). While traditional Equivalent Circuit Models (ECM) are typically parameterized and validated for a specific range of working conditions (temperature, current and etc.), PECM is able to adapt itself to any working condition in real time. Established in the form of a combination of linear and nonlinear piecewise functions, the model parameters are continuously adjusted based on the measurement of voltage, current, and temperature. Another advantage of PECM is it does not require any prior tests in the lab, for example the Open Circuit Voltage (OCV) test which is time consuming and needs to be calibrated when aged. PECM is accurate, flexible and efficient. It has been validated for different battery chemistries, duty cycles, and temperatures. Furthermore, PECM comes with the State of Charge (SOC) and State of Health (SOH) estimation, which is shown in the model validation process and the degradation study. The results demonstrate that the piecewise parameter adaptation proposed in this paper can be applied to a range of different battery chemistries and at different aged states.

Diffusion-aware voltage source: An equivalent circuit network to resolve lithium concentration gradients in active particles

Traditional equivalent circuit models (ECMs) have difficulties in estimating battery internal states due to the lack of relevant physics, such as the lithium diffusion in active particles. Here we configure a circuit network to describe the lithium diffusion and define it as a new high-level circuit element called diffusion-aware voltage source. The circuit representation is proven equivalent to the discretized diffusion equation. The new voltage source gives the electrode potential as a function of the surface concentration and thus automatically incorporates the diffusion overpotential. We show that an ECM with the proposed diffusion-aware voltage sources (called “shell ECM”) can reproduce the single particle model simulation results, making it a trustworthy easy-to-implement substitute. Furthermore, the simplest shell ECM consisting of a single diffusion-aware voltage source and a resistor is validated against experimental constant-current discharges at various rates. The diffusion-aware voltage source can be used to measure diffusivity by fitting the diffusion resistance against experimental data. The viability of the shell ECM for onboard usage is confirmed by implementation into a battery management system of WAE Technologies. By tracking the internal concentration states, the shell ECM demonstrates robustness to dynamic applied-current profiles.

Joint Analysis of Front-Door and Back-Door Couplings of PIN Limiter Based on Improved Equivalent Circuit Model

Based on the previous research on electromagnetic pulse coupling, which pays more attention to the front-door coupling or the back-door coupling alone, this paper analyzes the influence of an electromagnetic pulse on electronic devices and systems through the joint analysis of front-door and back-door couplings using the finite-difference time-domain method (FDTD). This specific measure is used to simplify the front-door coupling to the voltage source injection, which occurs simultaneously with plane wave irradiation. This coupling scheme of the front door and back door with the voltage source and plane wave acting simultaneously is rarely seen in previous analyses, which also gives consideration to the working state of the circuit. Although the equivalent circuit model is widely used, it cannot effectively reflect the working state of the diode circuit under the conditions of large injection and high frequency. In view of the limited application scenarios of the traditional equivalent circuit model, which cannot accurately describe the internal response characteristics of the diode under different electromagnetic pulse coupling, this paper introduces an improved equivalent circuit model based on the physical model. Taking the Positive Intrinsic-Negative (PIN) limiter as the target, this paper analyzes the influence of the front-door and back-door joint coupling on its performance under different electromagnetic pulses and then gives protection suggestions.

Joint state estimation of lithium-ion batteries combining improved equivalent circuit model with electrochemical mechanism and diffusion process

Accurate state estimation plays a key role for guaranteeing the safety and reliability of lithium-ion batteries. This paper develops a novel joint state estimation method for lithium-ion batteries based on a hybrid model combining improved equivalent circuit model (IECM) with electrochemical mechanism and diffusion process, it mainly includes state-of-charge, state-of-health, state-of-power and state-of-energy. Firstly, an IECM by combining the internal electrochemical mechanism and traditional equivalent circuit model is established to simulate the battery dynamic characteristics. The model parameters are offline identified by an electrochemical mechanism decoupling approach and online updated with the battery aging. Next, a hybrid model is presented by combining the diffusion process-based empirical aging model and the IECM, a co-estimation algorithm for state-of-charge and state-of-health by applying the dual extended Kalman filter is proposed. Then, the peak current is online calculated to evaluate the state-of-power under the model limitation, and the future working condition is predicted to evaluate the state-of-energy. Finally, several case studies are implemented to verify the effectiveness of developed method, the results indicate that the proposed state joint estimation method has higher accuracy and stronger robustness, and the root mean square error does not exceed 1 % with the battery aging.

Modeling With RTS Noise Characterization of Novel Embedded Photogate Single-Photon Avalanche Diode for Circuit Simulations

Single-photon avalanche diodes (SPADs) are widely used for weak light detection due to their high gain and high sensitivity. Unfortunately, SPAD devices have random telegraph signal (RTS) noise during the avalanche transition phase, which makes circuit design more difficult. Therefore, the modeling of RTS noise in SPAD devices is of great significance for the design of signal processing circuits. However, RTS noise is not included in the traditional equivalent circuit model. In response to the above problems, this paper implements an equivalent circuit model with RTS noise based on the Cadence. The model is built based on the basic components in the library, and it has strong application universality. The model is validated in a novel embedded photogate SPAD device (EP-SPAD). It accurately simulates the RTS noise and IV characteristics of the EP-SPAD device. In addition, the threshold voltage of EP-SPAD device operating in Geiger mode is precisely defined based on the characteristics of RTS noise. When the reverse bias voltage is increased from 0 V to 15 V, the IV characteristics of the model are consistent with the EP-SPAD device.

Lebesgue Sampling-Based Li-Ion Battery Simplified First Principle Model for SOC Estimation and RDT Prediction

The state-of-charge (SOC) estimation and remaining-dischargeable-time (RDT) prediction are critical and challenging to safe operation of Li-ion batteries. The main challenges are the limited accuracy of traditional equivalent circuit model and computation-inefficiency of electrochemical battery models. To address this problem, this article proposes a Lebesgue-sampling-based extended Kalman filter (LS-EKF) approach that integrates the high fidelity of a simplified first principle (SFP) model with the low computation of Lebesgue sampling (LS) in a Bayesian estimation framework. In this framework, the SFP model is first introduced along with its design and validation. The LS-EKF is employed with the SFP model to estimate the SOC and predict the RDT. The proposed method is verified with a series of experiments under different operating conditions. The results and comparisons demonstrate the effectiveness of the proposed method in terms of the accuracy of estimation and prediction, as well as the computational efficiency.

The state of health estimation of lithium-ion batteries based on data-driven and model fusion method

State of health (SOH) estimation of lithium-ion batteries is widely concerned. Currently, electric vehicles are rarely complete discharging in practical application, which remains lots of electricity and reduces constant current charging time. Therefore, this phenomenon hinders the applications of many traditional methods that require a complete constant current charging process. In this paper, we put forward a data-driven and model fusion method for SOH estimation based on constant voltage charging process (CVCP). Firstly, an improved equivalent circuit model (IECM) is established based on the current-time data of the CVCP. Secondly, Pearson correlation coefficient describes the strong mapping relationship between model parameters and SOH, so the model parameters are used as health indicators. Then, SOH prediction model is established by back propagation neural network whose model parameters are optimized by improved particle swarm optimization algorithm. Thirdly, considering time-consuming problem, a new scheme based on the incomplete CVCP that combine time constants prediction model and SOH prediction model is adopted. Finally, comparative results show that proposed IECM has the higher current estimation accuracy than traditional equivalent circuit models for different batteries. The SOH maximum errors of proposed method in different temperatures and data lengths are both within 2%.

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

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

Comparative Study on Improved and Traditional Equivalent Circuit of Long Primary Double-Sided Linear Induction Motor

Based on the quasi-two-dimensional (2D) field model of long primary double-sided linear induction motor (LPDLIM), an improved equivalent circuit model is proposed. First, the traditional equivalent circuit of LPDLIM is reviewed. Second, the skin effect correction coefficients for the secondary equivalent resistance and excitation reactance, and the secondary leakage inductance are derived. Moreover, an improved equivalent circuit model for LPDLIMs is presented, in which the leakage reactance of the secondary is considered, and the excitation reactance and secondary resistance are modified by the correction coefficients independently. Then, the slip frequency characteristics of various effect forces and variations of forces under different operations and mechanical air gap width are presented. Finally, the calculated forces by the proposed equivalent circuit are validated by the finite element method results and also compared with that of the traditional equivalent circuit model.

Quantitative analysis of internal polarization dynamics for polymer electrolyte membrane fuel cell by distribution of relaxation times of impedance

Investigating and interpreting each internal polarization dynamics that occurs in the polymer electrolyte membrane fuel cell is significant. Traditional equivalent circuit model fitting by nonlinear least-squares relies on prior model assumptions and initial value selection of components. In this paper, the distribution of relaxation times methodology with powerful separating ability is applied to reveal a more precise analysis of polarization processes. First, the electrochemical impedance spectroscopy under a broad of operating conditions is carried out. Four polarization dynamics related to oxygen transfer, charge transfer of the oxygen reduction, proton transfer inside cathode ionomer, and interface contact process between catalyst layer and membrane (perhaps, including anode oxidation reaction) are effectively extracted. Then, a fourth-order equivalent circuit model established via distribution of relaxation times results is introduced to quantify the loss of each polarization process. Based on this, for the first time, the sensitivity of each polarization loss against operating conditions is analyzed by the multiple stepwise regression analysis, and its application on vehicular fuel cell system control is discussed. Afterward, the distribution of relaxation times is also first to explore the loss and variation trend of each polarization process under flooding, membrane drying, and air starvation fault, where each failure type contains at least eight test sequences. These efforts represent a comprehensive and systematic guideline for fuel cells using distribution of relaxation times, which can also guide the study of degradation mechanisms, optimization design of materials, and even other electrochemical energy sources.

A Novel, Improved Equivalent Circuit Model for Double-Sided Linear Induction Motor

A novel, improved equivalent circuit model of double-sided linear induction motors (DLIMs) is proposed, which takes the skin effect and the nonzero leakage reactance of the secondary, longitudinal, and transverse end effects into consideration. Firstly, the traditional equivalent circuit with longitudinal and transverse end effects are briefly reviewed. Additionally, the correction coefficients for longitudinal and transverse end effects derived by one-dimensional analysis models are given. Secondly, correction factors for skin effect, which reflects the inhomogeneous air gap magnetic field vertically, and the secondary leakage reactance are derived by the quasi-two-dimensional analysis model. Then, the proposed equivalent circuit is presented, and the excitation reactance and secondary resistance are modified by the correction coefficients derived from the three analytical models. Finally, a three-dimensional (3D) finite element model is used to verify the proposed equivalent circuit model under varying air gap width and frequency, and the results are also compared with that of the traditional equivalent circuit models. The calculated thrust characteristics by the proposed equivalent circuit and 3D finite element model are experimentally validated under a constant voltage–frequency drive.

Once again about the indivisibility of the scattered inductance of the transformer

Purpose. The purpose of the article is to show the inadequacy of the traditional T-shaped equivalent circuit for modeling transformer operations with saturated core. The aim is to point out the unreasonableness of the separation of the transformer leakage inductance into components. The aim is also to explain the need to apply the П-shaped transformer equivalent circuits to transformers with two and three windings with finite radial thickness.
 Methodology. Analysis of magnetic fields in the transformer window and simulation of transient processes in equivalent circuits of the transformer using a preprocessor ATPDraw to the program ATP.
 Findings. The unfoundedness of the well-known T-shaped transformer equivalent circuit is shown. Differences in the processes in the core legs and yokes when transformer is connected to the network and during short circuits of the windings are noted. Equivalent circuits of a transformer with two and three windings of finite thickness are proposed, reproducing these differences.
 Originality. The absence of physical meaning in dividing the transformer leakage inductance into components is stated. The advantages of the П-shaped equivalent circuit are shown when calculating inrush currents accompanying the transformer switching to the network on its inner and outer windings.
 Practical value. We show theoretical insolvency and practical unsuitability of the Т-shaped equivalent circuit for studying transformer operations accompanied by saturation of the magnetic circuit. Advantages of the П-shaped equivalent circuit are clarified.

Global parametric sensitivity analysis of equivalent circuit model based on Sobol’ method for lithium-ion batteries in electric vehicles

It is well established that the model parameters of an equivalent circuit model are crucial to improve the accuracy and stability of state estimation for lithium-ion batteries. However, real-time updates for all parameters in a traditional equivalent circuit model over the entire life cycle of the lithium-ion batteries are computationally costly owing to the excessive calculations required. To address this issue, in this study, global parameter sensitivity analysis of a typical equivalent circuit model, namely 2RCH (second-order resistance-capacitance with one-state hysteresis), is performed on two types of lithium-ion batteries using the Sobol’ method to investigate the global parametric sensitivity under different aging degrees. Then, the 2RCH model is simplified. The simplified 2RCH model only requires half of the model parameters to be updated regularly compared with the original 2RCH model, while the other model parameters are fixed; this significantly reduces the extent of calculations required for state estimation. Our experimental results indicate that: (1) the first- and higher-order sensitivity indices of each parameter are appropriate; (2) the simplified 2RCH model has almost the same accuracy as the original model wherein all parameters are updated, but requires only half the calculations as that in the original model. Hence, our proposed approach is of great significance as it can reduce at least half of the calculation in the state estimation over the whole battery life cycle under dynamic conditions. Also, the proposed model can improve the global accuracy of battery state estimation, which is beneficial to improve the life of battery and electric vehicle.

Choosing the type of equivalent circuit of traction substation when calculating short-circuit currents in 25 kV power supply system

When calculating short circuit currents in the traction network, it is necessary to take into account the input resistance of the traction substation, including the resistance of the transformers of the substation and the resistance of the power supply system. The input resistance during short circuit is determined based on the equivalent circuit of the external power supply system, of which this traction substation is an integral part. Traditionally equivalent circuit of a three-phase system has the form of a star, in which the resulting resistances in each phase are connected in series with a source of phase electromotive force, and these sources have a common point. Another equivalent circuit in the form of a triangle is possible, in which on each side the resulting resistances are connected in series with the source of linear electromotive force. It is important to note that neither one nor the other type of equivalent circuit is determined by the connection scheme of the transformer windings of the traction substation. It is only necessary to take into account the absence of a circuit for zero sequence currents. All elements of the equivalent circuit, as is known, should be brought to uniform basic conditions. If the parameters of these elements are expressed in named units, then the basic values are the effective voltage values of the main stage and the rated power of the power transformer of the traction substation. If the components of one and the other equivalent circuits are reduced to one stage of the operating voltage, for example 27.5 kV, then for the same elements of the power supply system, the resistance values in the equivalent circuit in the form of a triangle are three times larger than in the equivalent circuit in the form of a star. In this case, the input resistances of the traction substation for the one and the other equivalent circuits are absolutely identical. Therefore, in the calculation of short circuit currents of the traction network, you can use any of these equivalent circuits of the power supply system and traction substation. Formulas for calculating the resistances of the elements of the power supply system and electrical installations, given in the standards, manuals and reference books, relate to the equivalent circuit of the short circuit in the form of a star. When using an equivalent circuit in the form of a triangle, these resistances must first be tripled, and then divided by three when calculating the short-circuit currents. The meaninglessness of such an operation is obvious. The equivalent circuit of the traction substation and the external power supply system in the form of a triangle when calculating short circuits in the traction network has no advantages compared to the traditional equivalent circuit in the form of a star. The information on the linear currents on the primary and secondary windings of the traction substation transformer during a short circuit in the traction network is given, which is necessary to select the settings of its relay protection kit.

Prediction of I-V Characteristic Curve for Photovoltaic Modules Based on Convolutional Neural Network.

Photovoltaic (PV) modules are exposed to the outside, which is affected by radiation, the temperature of the PV module back-surface, relative humidity, atmospheric pressure and other factors, which makes it difficult to test and analyze the performance of photovoltaic modules. Traditionally, the equivalent circuit method is used to analyze the performance of PV modules, but there are large errors. In this paper—based on machine learning methods and large amounts of photovoltaic test data—convolutional neural network (CNN) and multilayer perceptron (MLP) neural network models are established to predict the I–V curve of photovoltaic modules. Furthermore, the accuracy and the fitting degree of these methods for current–voltage (I–V) curve prediction are compared in detail. The results show that the prediction accuracy of the CNN and MLP neural network model is significantly better than that of the traditional equivalent circuit models. Compared with MLP models, the CNN model has better accuracy and fitting degree. In addition, the error distribution concentration of CNN has better robustness and the pre-test curve is smoother and has better nonlinear segment fitting effects. Thus, the CNN is superior to MLP model and the traditional equivalent circuit model in complex climate conditions. CNN is a high-confidence method to predict the performance of PV modules.

Improved gyrator–capacitor model considering eddy current and excess losses based on loss separation method

The traditional equivalent circuit model based on the reluctance–resistance analogy method is used to model electromagnetic equipment in power systems. However, this model has unreasonable analogy, incomplete magnetic circuit information, and is difficulty to expand. This study proposes an improved gyrator–capacitor (G–C) model and its parameter extraction method for the modeling of electromagnetic devices in power systems. An improved G–C model considering eddy current and excess losses is proposed on the basis of the loss separation method and by utilizing the physical concept of resistance. On the basis of the proposed model, simple calculation methods of the instantaneous loss power and density of the core are presented. A parameter extraction method considering the fitting effect of the entire hysteresis loop and special points is proposed in accordance with the idea of curve fitting. The proposed model and its parameter extraction method are verified by comparing the calculated results with the measured results.

An accurate parameters extraction method for a novel on-board battery model considering electrochemical properties

Accurate battery models are essential for the assessment of battery states and performance. Traditional equivalent circuit model (ECM), e.g. second-order RC model, cannot imitate non-linear characters of Lithium-ion battery especially in low state of charge (SOC) area. Considering the advantages of battery electrochemical and ECM, the paper proposes an electrochemistry-based equivalent circuit model (E-ECM). With only two parameters more than second-order RC model, E-ECM can simulate battery voltage response better. Next, different from the previous model parameters optimization method, a decoupling parameters extraction (DPE) method is studied to derive the more appropriate model parameters for the proposed E-ECM first. The DPE method is believed to relate to battery electrochemical characters. Experiment results show that the obtained E-ECM is of a good performance no matter in the dynamic working conditions, or constant current working condition, especially in low SOC area. Moreover, the proposed E-ECM is able to describe battery rate capability with high accuracy.

Modeling Study for Li-ion Batteries Considering High-frequency Inductance Characteristics Based on Electrochemical Impedance Spectroscopy

As a non-destructive test method, electrochemical impedance spectroscopy (EIS) has been widely used in the analysis and diagnosis of Li-ion batteries in recent years. But the study of the high-frequency characteristics of Li-ion batteries is still not enough and the performance of Li-ion batteries at high frequency is not the same with that of the pure capacitance or pure inductance. Based on EIS, a fractional equivalent circuit model considering high-frequency inductance characteristics is established in frequencies from 10mHz to 10kHz in this paper. Then the model is verified and the parameters of the circuit are explored by using differential evolution (DE) algorithm and fractional-order numerical operations. Compared with the traditional equivalent circuit model, a fractional-order model based on EIS can not only describe the characteristics of the battery more comprehensively but also reduce the number of parameters because each component can simulate a certain physicochemical process of Li-ion batteries. The dominant process of the battery reaction is diverse in different frequency bands and therefore the structure of the developed model can be simplified accordingly. For the high-frequency inductive analysis of the battery, results show that the battery's 'inductance-like' phenomenon has a certain relationship with the frequency. This discovery might be implemented in a power electronic circuit to improve understanding of how batteries react to working condition of high-frequency.