Empirical Equivalent Circuit Research Articles

Construction and Analysis of Battery Equivalent Circuit Model Considering Liquid Phase Lithium Ion Diffusion Under High-Rate Conditions

In order to obtain the internal state of lithium-ion battery quickly and accurately, the problem that the internal state of the battery is difficult to estimate quickly and accurately is solved. The discharge performance of lithium ion is affected by the electrode current during the charge and discharge process. This paper analyzes the key factors of the electrochemical model at high rate, considers the change of lithium ion concentration in the liquid phase of the battery, integrates the electrochemical mechanism and the equivalent circuit, and establishes a mechanism equivalent circuit model with more computational advantages through circuit elements. The equivalent circuit model can describe the physical characteristics of the lithium battery. Under high rate constant current and dynamic conditions, the model shows good electrical characteristics. Compared with the traditional empirical equivalent circuit model, the accuracy of the model is improved, and the state quantity is reduced by 15 compared with the electrochemical model. The model is of great significance in practical application.

Physics-Based Equivalent Circuit Model for Lithium-Ion Cells via Reduction and Approximation of Electrochemical Model

<div class="section abstract"><div class="htmlview paragraph">Physics-based electrochemical models and empirical Equivalent Circuit Models (ECMs) are well-established and widely used modeling techniques to predict the voltage behavior of lithium-ion cells. Electrochemical models are typically very accurate and require relatively little experimental data to calibrate, but present high mathematical and computational complexity. Conversely, ECMs are more computationally efficient and mathematically simpler, making them well-suited for applications in controls, diagnosis, and state estimation of lithium-ion battery packs. However, the calibration process requires extensive testing to calibrate the parameters of the model over a wide range of operating conditions.</div><div class="htmlview paragraph">This paper bridges the gap between these two classes of models by developing a method to analytically define the ECM parameters starting from an already-calibrated Extended Single-Particle Model (ESPM). The governing equations of the ESPM were reduced via model order reduction, linearization and by introducing approximations to yield the mathematical structure of a second order ECM. This allowed for analytically defining the parameters of the resulting ECM, without resorting to complex lookup tables and related extensive testing for calibration. The newly defined electrochemistry-based ECM (E-ECM) saw less than 1 mV RMS error increase compared to the ESPM voltage prediction across several test profiles.</div></div>

Novel method for the parameterization of a reliable equivalent circuit model for the precise simulation of a battery cell's electric behavior

This article presents a novel approach to extract the equivalent circuit model parameter from a pulse test. The presented results corroborate that this novel heuristic methodology can very accurately fit the voltage response of the battery, while drastically reducing the dependence of the parametrization on set boundary conditions and initial guess values. The method's robustness is verified by fitting the voltage response of a mock battery model with pre-defined parameters. It could be shown that the suggested method is able to precisely extract the set parameters from the simulated voltage. Furthermore, the model values obtained from the test of a lithium ion battery cell correlate with physical parameter and other investigation methods like the calculation of the distribution of relaxation times (DRT). As a result, an accurate equivalent circuit model of the cell was created. The restriction as to universal validity of the empirical equivalent circuit model was significantly reduced by limiting the voltage of the RC element with highest time constant. Finally, a robust battery cell model with only a minor root-mean-square error of 1.30% was obtained. ResultA new method for the precise parameterization of an equivalent circuit model from pulse tests is presented. The robustness of such equivalent circuit models is increased by limiting the voltage of the RC element with the highest time constant. Overall, a precise, reliable model of a lithium-ion battery cell is created.

Control-Oriented Modeling of Lithium-Ion Batteries

Abstract Battery management systems (BMSs), which monitor and optimize performance while ensuring safety, require control-oriented models, i.e., models tailored to the design and implementation of estimation and control algorithms. Physics-based electrochemical models describe detailed battery phenomena, but are too computationally intensive for use in estimation and control applications. Single particle models (SPMs), which retain some of the physics of electrochemical models, are often used for control-oriented battery modeling since they are computationally efficient; however, they are only valid over very low frequency ranges and C-rates. Empirical equivalent circuit models (ECMs) are also used for control-oriented battery modeling since they are computationally efficient and can describe battery behavior over wide frequency ranges; however, they provide no physical understanding of the battery and, therefore, have limited applicability. Further, fractional order terms (e.g., Warburg impedances) are often employed, making the models unwieldy for use in the time domain. This work provides a control-oriented battery model that combines the benefits of SPM and ECM models, while overcoming their limitations. The proposed model incorporates some of the battery physics found in electrochemical models, can easily be used in both the time and frequency domains, and describes battery behavior over its entire frequency range. A linearized single particle model, which incorporates key electrochemical parameters, is used for modeling battery physics at very low frequencies. For low frequencies, integer-order linear systems are used to approximate diffusion physics described by Warburg impedances, and high frequency behavior is modeled by the double layer capacitance effect. The proposed battery model is more computationally efficient than full electrochemical models since it does not require the solution of PDEs, is accurate for a wider frequency range than the SPM considered in this paper, and does not suffer from the unwieldiness and limited applicability of empirical ECMs. The model is validated in the time and frequency domains via a comparison to pseudo-two-dimensional (P2D) model simulations and experimental data.

A novel nonlinear large‐signal statistical model of GaN HEMT used in S‐band power amplifier design and yield estimation

SummaryA novel GaN high‐electron mobility transistor (HEMT) nonlinear large‐signal statistical model based on empirical equivalent circuit is proposed in this paper. Thirty‐four GaN HEMTs from 10 batches are measured, and all the parameters of the large‐signal model are extracted by in‐house parameter extraction program. We choose six most sensitive parameters of the drain‐source current model and the gate charge model. The statistical method is modeled by using a symbolic processing method to change the range of the six parameters. The statistical model is implemented in Agilent ADS software for validation. A S‐band GaN HEMT power amplifier is designed by using the established statistical model for demonstration purpose. The results show that good accuracy has been achieved by comparing measured and simulated output power (Pout) and power added efficiency (PAE). So it has been proven that this method is suitable for GaN HEMT power amplifier design and yield estimation. Copyright © 2016 John Wiley & Sons, Ltd.

A GaN HEMTs Nonlinear Large-Signal Statistical Model and Its Application in S-Band Power Amplifier Design

A GaN HEMTs nonlinear large-signal statistical model based on empirical equivalent circuit including nonlinear electrothermal effect and trapping effects is proposed in this letter. The electrothermal model is constructed by one stage nonlinear R-C electrothermal network, and the trapping effects is modeled by effective gate (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gseff</sub> ) bias based on Angelov model. Thirty-four GaN HEMTs from 10 batches are measured and all the parameters in the large-signal model are extracted by in-house parameters extraction program. The statistical method is modeled by combining principal component analysis, factor analysis, and multiple regressions modeling techniques. The statistical model is implemented in Agilent-ADS and the Monte Carlo simulation is fulfilled for validation. Two S-band GaN HEMT power amplifiers are designed by using the established statistical model for demonstration purpose. The results show that good accuracy have been achieved by comparing measured and Monte Carlo simulated output power (Pout) and power added efficiency (PAE). So this method is proved to be suitable for GaN HEMT power amplifier's design and yield estimation.

Nanofilament Dynamics in Resistance Memory: Model and Validation.

Filamentary resistive random-access memory (ReRAM) employs a single nanoscale event to trigger a macroscopic state change. While fundamentally it involves a gradual electrochemical evolution in a nanoscale filament that culminates in an abrupt change in filament's resistance, understanding over many length and time scales from the filament level to the device level is needed to inform the device behavior. Here, we demonstrate the nanoscale elements have corresponding elements in an empirical equivalent circuit. Specifically, the filament contains a variable resistor and capacitor that switch at a critical voltage. This simple model explains several observations widely reported on disparate filamentary ReRAMs. In particular, its collective system dynamics incorporating the power-law time-relaxation of the variable capacitance can accurately account for the responses of variously sized single-filament HfOx ReRAMs to DC/quasi-static and pulse electrical stimulation, exhibiting Avrami-like switching kinetics and a pulse-rate dependence in on/off voltages.

Studying electron transfer reaction at the Au/n-decanethiol/aqueous solution of NaNO3 interface by electrochemical impedance spectroscopy

The electrochemical behavior of the gold/electrolyte interface in aqueous 1 M NaNO3 solutions in the presence of an organic monolayer of n-decanethiol (CH3(CH2)9S) is studied by electrochemical impedance spectroscopy in the frequency range of 10–105 Hz and also by cyclic voltammetry. It is experimentally shown that in the potential interval from 0 to −0.5 V (vs. SCE), the dense monolayer film decreases the measured current density approximately 40-fold. The measured capacitance falls down to 1–2 μF/cm2. Based on the analysis of impedance characteristics acquired with the use of empirical equivalent circuits comprising ideal and nonideal analogues of electric circuits, the tentative estimates of the thickness of organic monolayers formed on Au electrodes with various roughness factors are obtained. Using the complex nonlinear regression (CNLS) method and a model of microarray electrode, the porous structure of adsorbed monolayers is revealed and the transition frequency of interfaces under study is determined. The degree of inhibition of the electron transfer across the Au/n-decanethiol/solution interface is determined by comparing the rate constants for the Ru[(NH3)6]3+/2+ redox process on clean and modified electrodes. The acquired results are compared with available literature data.

Model-Based Electrochemical Estimation and Constraint Management for Pulse Operation of Lithium Ion Batteries

High-power lithium ion batteries are often rated with multiple current and voltage limits depending on the duration of the pulse event. These variable control limits, however, are difficult to realize in practice. In this paper, a linear Kalman filter based on a reduced order electrochemical model is designed to estimate internal battery potentials, concentration gradients, and state-of-charge (SOC) from external current and voltage measurements. A reference current governor predicts the operating margin with respect to electrode side reactions and surface depletion/saturation conditions responsible for damage and sudden loss of power. The estimates are compared with results from an experimentally validated, 1-D, nonlinear finite volume model of a 6 Ah hybrid electric vehicle battery. The linear filter provides, to within ~ 2%, performance in the 30%-70% SOC range except in the case of severe current pulses that draw electrode surface concentrations to near saturation and depletion, although the estimates recover as concentration gradients relax. With 4 to 7 states, the filter has low-order comparable to empirical equivalent circuit models commonly employed and described in the literature. Accurate estimation of the battery's internal electrochemical state enables an expanded range of pulse operation.

Electrochemical behavior of silver single-crystal electrodes in 1 M NaNO3 solution in the absence and in the presence of decanethiol films

The surface properties of silver single-crystal faces (111) and (210) in 1 M NaNO3 aqueous solution in the absence and in the presence of monolayer n-decanethiol (DT) films are studied by the methods of cyclic voltammetry and electrochemical impedance using the meniscus contact technique. It is experimentally shown that, in the potential range from 0 to −0.5 V, the faradaic processes are absent and low currents are recorded on the unmodified silver surfaces. It is shown that the DT molecules, which are adsorbed on the nonoxidized surfaces of silver faces, spontaneously form (during 72 h) compact structurized films. The films are stable in the air and in the electrolyte solutions and totally block the surfaces of both faces. The impedance spectra, which were measured for each interface in a wide range of frequencies, are analyzed and interpreted. The measurements were performed by the use of the corresponding empirical equivalent circuits containing perfect and imperfect analogs of electrical circuits; complex nonlinear least squares (CNLS) regression method was applied for the calculations. The capacitance, ohmic resistance, and adsorbed monolayer thickness were estimated.

Two-Port Electromechanical Model for Bulk-Piezoelectric Excitation of Surface Micromachined Beam Resonators

A small-signal model that describes the energy exchange between surface micromachined beams and bulk-lead zirconium titanate (PZT) actuators attached to the silicon substrate is presented. The model includes detection of acoustic waves launched from electrostatically actuated structures on the surface of the die, as well as their actuation by bulk waves generated by piezoelectric ceramics. The interaction is modeled via an empirical equivalent circuit, which is substantiated by experiments designed to extract the model parameters. The equivalent model is valid for cases where the beam resonance frequency is much smaller than the thickness mode resonance of the PZT/silicon stack. In this paper, the resonance frequency of the beams ranges between 200 and 300 kHz. As energy transfer between bulk-PZT and electrostatic actuated beam resonators must be reciprocal for small signals, this paper uses the extracted equivalent model to describe the physical sources of error that account for discrepancies in reciprocity.

Cathode reaction mechanism of porous-structured Sm0.5Sr0.5CoO3− and Sm0.5Sr0.5CoO3−/Sm0.2Ce0.8O1.9 for solid oxide fuel cells

Abstract The cathode reaction mechanism of porous Sm0.5Sr0.5CoO3−δ, a mixed ionic and electronic conductor (MIEC), is studied through a comparison with the composite cathode Sm0.5Sr0.5CoO3−δ/Sm0.2Ce0.8O1.9. First, the cathodic behaviour of porous Sm0.5Sr0.5CoO3−δ and Sm0.5Sr0.5CoO3−δ/Sm0.2Ce0.8O1.9 are observed for micro-structure and impedance spectra according to Sm0.2Ce0.8O1.9 addition, thermal cycling and long-term properties. The cathode reaction mechanism is discussed in terms of frequency response, activation energy, reaction order and electrode resistance for different oxygen partial pressures p(O2) at various temperatures. Three elementary steps are considered to be involved in the cathodic reaction: (i) oxygen ion transfer at the cathode–electrolyte interface; (ii) oxygen ion conduction in the bulk cathode; (iii) gas phase diffusion of oxygen. A reaction model based on the empirical equivalent circuit is introduced and analyzed using the impedance spectra. The electrode resistance at high frequency (Rc,HF) in the impedance spectra represents reaction steps (i), due to its fast reaction rate. The electrode resistance at high frequency is independent of p(O2) at a constant temperature because the semicircle of Rc,HF in the complex plane of the impedance spectra is held constant for different values of p(O2). Reaction steps (ii) and (iii) are the dominant processes for a MIEC cathode, according to the analysis results. The proposed cathode reaction model and results for a solid oxide fuel cell (SOFC) well describe a MIEC cathode with high ionic conductivity, and assist the understanding of the MIEC cathode reaction mechanism.

Combined Deconvolution and CNLS Fitting Approach Applied on the Impedance Response of Technical Ni ∕ 8YSZ Cermet Electrodes

A high-resolution impedance study of the hydrogen oxidation in (yttria-stabilized zirconia) cermet anodes has been realized in consideration of a broad range of operating conditions (temperature and partial pressure of fuel gas components , , , He). A major problem in this respect concerns the origin and physical interpretation of empirical equivalent circuits used to fit the experimental data. We applied a two-stage approach for the evaluation of the impedance data: (i) at first, by the deconvolution of a distribution function of relaxation times (DRT), four different processes and their characteristic relaxation times have been identified. Two processes at frequencies represent a gas-conversion process or, respectively, a gas diffusion, whereas two processes at higher frequencies are associated with the electro-oxidation of hydrogen at active sites, including the charge transfer reaction and the ionic transport. (ii) Subsequently, the last mentioned processes were fitted to a “transmission line” model describing the electronic and ionic transport properties of the cermet. The high resolution of the DRT combined with the numeric accuracy of the complex nonlinear least square (CNLS) fit enabled us to determine (i) the effective ionic conductivity of the cermet, (ii) the spatial extension of the electrochemically active area adjacent to the electrolyte/electrode interface, and (iii) the charge transfer resistance and its thermal activation energy.

Complete capturing of the electrode impedance at hydrogen, Ni/PSZ with an empirical equivalent circuit

As the first step to understand the electrode impedance at gas, electrode/solid-electrolyte systems, the complete capturing of electrode impedance at H 2, Ni(NiO)/stabilized zirconia was conducted with an empirical equivalent circuit proposed for O 2, Pt/stabilized zirconia. Impedance plots of various depressed semicircles and those that overlapped were completely duplicated with the circuit and compacted into values of three parameters for the impedance at the electrode process and two parameters for a diffusion through a porous layer. The former three were affected by the temperature and the partial pressure of H 2O but not by the thickness of the electrode. It was suggested that the impedance plot of a single depressed semicircle may sometimes contain relatively large diffusion impedance.

Mathematical approaches to electron device modelling for non‐linear microwave circuit design: State of the art and present trends

AbstractThe accuracy of CAD techniques for the design of non‐linear microwave circuits is strongly dependent on the features of the models used for the characterization of electron devices (i.e. MESFET, bipolar transistors, diodes etc.,.). At present, empirical equivalent circuits are widely used. These models, which are in many cases sufficiently accurate, require, however, quite refined numerical and measurement techniques to extract from measured data the parameters of a model which is strongly dependent on the particular physical structure of each device.Moreover, when using equivalent circuit models, the design of non‐linear microwave circuits must be carried out by using numerical optimization techniques. In this respect a simple mathematical model described in the frequency domain in terms of explicit equations between the electrical variables, would be preferable for the designer. Mathematical models, in fact, allow quite easy, direct procedures for circuit design. This paper deals with the problem of mathematical modelling of electron devices operating under large‐signal conditions at microwave frequencies. In particular, mathematical models based on the describing‐function and Volterra‐series approach are considered also taking into account their application to circuit design. The advantages of a recently proposed mathematical modelling approach based on mild assumptions valid for most types of electron devices, are also discussed in the paper.

Hysteresis motor with overexcitation and solid-state control

The overexcitation for a short period of a hysteresis motor when running synchronously gives a reduction in stator current and an increase in pull-out torque. The physical concept of the phenomenon is briefly discussed and an empirical equivalent circuit incorporating a residual flux voltage is established which gives reasonable agreement with measured values. Methods of implementation of the technique are described, including delta-star starting and two solid-state-control devices. It is shown that, with short-duration overexcitation, harder magnetic materials may be used for the rotor, thus increasing the machine rating for a given frame size.

Current oscillations and microwave emission in indium antimonide

The oscillatory properties of indium antimonide subjected to comparatively high applied parallel electric and magnetic fields at 77°K have been studied. In particular, the low-frequency oscillations in the current have been characterized by an empirical equivalent circuit. This circuit has been used to help clarify the relationship between these current oscillations and the microwave emission which is also observed under the same experimental conditions. This work suggests that there are at least two separate mechanisms of microwave emission, one that is associated with and requires low-frequency oscillations in the sample current, and one which is not associated with and is independent of low-frequency oscillations in the sample current.