Thevenin model

In this section, we propose two eqnivalent electrical circuits used to model the electrical behavior of lithium batteries the model developed by FreedomCar and the Thevenin model. 

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The Thevenin model is a relatively simple equivalent diagram for describing the electrical behavior of a battery. This model, represented by Figure 5.6, is frequently used because of its simphcity. It comprises an ideal voltage source Fq, an internal... 

The improved Thevenin model comprises a self-discharge resistance Rp, two resistances Ric and Rid for ohmic losses in voltage during charging and discharging respectively, two resistances Rco and Rio to model the electrochemical voltage losses, a battery capacitor Cj, and a double-layer capacitor Q. 

According to this model, the SEI is made of ordered or disordered crystals that are thermodynamically stable with respect to lithium. The grain boundaries (parallel to the current lines) of these crystals make a significant contribution to the conduction of ions in the SEI [1, 2], It was suggested that the equivalent circuit for the SEI consists of three parallel RC circuits in series combination (Fig. 12). Later, Thevenin and Muller [29] suggested several modifications to the SEI model ... 

The interpretation of the Li abundance gap using a diffusion model has been questioned because of the observed absence of abundance anomalies of heavy elements in F stars (Boesgaard and Lavery 1986 Thevenin, Vauclair and Vauclair 1986 Tomkin, Lambert and Balachandran 1985) where Be has been observed to be underabundant. Such anomalies had been predicted on account of the diffusion calculations in the absence of any mass loss (Michaud et al. 1976, Vauclair et al. 1978b). It has recently been shown that even a very small mass loss was sufficient to reduce considerably any expected overabundance in F stars. On Fig. 2c of Michaud and Charland (1986), it is shown that a mass loss rate of 10 15 Mo yr-1 is sufficient to keep the Sr overabundance, below a factor of 1.5 while Sr would be expected to be more than 100 times overabundant in the absence of mass loss (Michaud et al. 1976). The presence of even a very small mass loss rate considerably limits any overabundance when the radiative acceleration and gravity are close to each other as is the case for heavy elements in stars cooler than Teff = 7000 K. The same small mass loss rate reduces the Li overabundance in stars of Teff = 7000 K or more where Li is supported. As shown in Fig. 4 of Michaud (1986), the same mass loss rate of 10 15 Mo yr 1 eliminates the Li overabundance of a factor of 10 expected in the absence of mass loss at Teff = 7000 K. It has now been verified that the presence of mass loss cannot increase the Li underabundance that diffusion leads to beyond a total factor of 30 underabundance. 

Thevenin s theorem states that a section of a linear circuit containing one or more sources and impedances can be replaced with an equivalent circuit model containing only one voltage source and one series-connected impedance, as shown in Figure 2.35. 

Detonation is a process of layer-by-layer, supersonic propagation of chemical reactions through an explosive (Figure 4.1). According to the generally accepted Zeldovich-von Neumann-Doering (ZND) model of detonation, chemical reactions occur at a definite rate in the chemical reaction zone, under the action of a shock wave (Baum et al., 1975 Berger and Viard, 1962 Cheret, 1979, 1993 Cook, 1958, 1974 Fickett and Davis, 1979 Johansson and Persson, 1970 Mader, 1979 Thevenin, 1978). 

Min BG, Kresh JM, Fich S, Kostis JB, Welkowitz W (1978) Relation between computed zero-load aortic flow and cardiac muscle mechanics. J. Biomech 80 227-235 Sandler J, Dodge HT (1963) Left ventricular tension and stress in man. Circ Res 13 91 Shastri SJ (1969) A thevenin equivalent model of the left ventricle derived from hemodynamic measurements obtained by use of a ventricular assist pump. Ph D Thesis, New Brunswick, NJ Rutgers Univ... 

Later Thevenin and Muller suggested several modifications to the SEI model (1) the polymer-electrolyte interphase (PEI) model in which the lithium in PC electrolyte is covered with a PEI composed of a mixture of LijCOj, P(PO),and LiClO, P(PO), is polypropylene oxide, formed by reduction-induced polymerization of PC (2) the solid-polymer-layer (SPL) model, where the surface layer is assumed to consist of solid compounds dispersed in the polymer electrolyte (3) the compact-stratified layer (CSL) — in this model the surface layer is assumed to be made of two sublayers. The first layer on the electrode surface is the SEI, while the second layer is either SEI or PEI. The first two... 

The modeling of an accumulator or battery of accumulators is a highly complex task. There are many different approaches, which will be more or less appropriate depending on the objectives reqnired of the model. In order to replicate electrical behavior similar to that of a battery, we nse a model in the form of an equivalent electrical circuit. Many different circuits are put forward in the existing body of literature Thevenin equivalent circnit, improved Thevenin equivalent circuit, FreedomCar, etc. In all cases, the parameters nsed for these models are determined experimentally. 

The Thevenin equivalent circuit is the simplest combination, since it is the association of an ideal voltage source and a resistor connected in series. This is a much more realistic way of modeling a lead-acid battery. Indeed, the resistor illustrates the voltage drop due to the current passing through the components of the battery. In the case of LABs, this instantaneous voltage drop mainly results from the low electrical conductivity of electrolyte and is proportional to the current. But, such a simple combination does not account for the polarization of the electrodes happening later on, when the battery is operated. 

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