Battery Modeling

Electrochemical properties and battery management of lithium metal and lithium-ion cells were analyzed using several different models. The electrochemical model developed by Doyle et al. [140-142] consists of six coupled, nonlinear differential equations whose solutions obtained from the Fortran program named 

The long term calendar life of lithium ion cells for satellite and standby applications was studied by Broussely et al. [150]. In experiments, the capacity evolution was tracked as a function of storage temperature. Cells containing either LiCo02 or 

Julien C, Nazri GA (1994) Solid state batteries materials design and optimization. Kluwer, Boston 

Goonan TG (2012) Lithium use in batteries. US Geological Survey Circular 1371, Reston, Virginia, http //pubs.usgs.gov/circ/1371/pdf/circl371 508.pdf 

Pistoia G (1994) Lithium batteries new materials, developments and perspectives. Elsevier, Amsterdam 

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Eig. 11. Typical discharge curve comparison for zinc—mercuric oxide batteries (-) model 325, HgO, and (-... 

The value of n is the only parameter in this equation. Several procedures can be used to find its value when the RTD is known experiment or calculation from the variance, as in /i = 1/C (t ) = 1/ t C t), or from a suitable loglog plot or the peak of the curve as explained for the CSTR battery model. The Peclet number for dispersion is also related to n, and may be obtainable from correlations of operating variables. 

Continurrm battery models consist of two scales, namely, the micro and the macro scale. The model eqrratiorrs are briefly described below. 

There are numerous advantages of using continuum models. They are widely used for system design and optimization. Continuum models tell us important information about the system, e g., discharge curves, state-of-health of the battery, cycle life behavior and subsequently capacity fade rate, etc. Battery models are also useful in predicting non-measurable internal variables such as solution phase concentration, solid phase concentration etc. This can be used to observe or measure buildup or loss of a certain chemical species within the domain of the battery and can be used efficient-... 

Similar to the concept described for the Oj-Hj cell system, the reductive activation of oxygen can be expected at the cathode in the presence of a suitable catalyst. On the basis of this zinc-air battery model, we have designed a number of catalytic systems from mixtures of zinc powder, carboxylic acid and various metal chlorides for oxygenations of alkanes and alkenes. In these catalytic systems, zinc powder works as the reductant as well as the electron conducting medium. The carboxylic acid works as a proton-conducting medium. Oxygen is reductively activated on the metal cations by protons from the carboxylic acid and electrons from zinc powder. 

Other adaptive systems are based on a comparison of the battery voltage with the calculated voltage of a battery model. The differences are used to adapt the parameters of the battery model. The parameters and state values of the model are used for SoC and SoH calculations. The principle of such a system is illustrated in Fig. 8.13. 

Other methods for parameter adaptation are known. The use of a Kahnan filter is the most popular one. The basis of such a filter is the battery model shown in Fig. 8.14. The Kalman filter takes the statistical knowledge of the parameter and the measurement into account. Applications are described in Refs. [16] and [17]. 

Fig. 8.14. Battery model used within a Kalman filter.

Battery Model GHK Constant Field Formulation GHK with Correction for Fixed Surface Charge Eyring Rate Theory Models of Ionic Currents Ion Pump Ion Exchangers Synapses Calcium as a Second Messenger... 

In order to extract thermal battery parameters from a measured impedance spectrum, a thermal model of the battery is necessary. This model reproduces the effects of heat capacity, thermal conductivity, heat exchange with environment, and internal losses generation. Transient simulation is then used to calculate an impedance spectrum for the battery model which is subsequently employed for parameter identification. 

The implemented battery model is the basis for the identification of thermal cell parameters. With the battery model, TIS measurements are simulated. The same sinusoidal heat excitation as in the experiment is apphed to the thermal battery model. Simulation results dehver thermal impedances for each frequency, which form an entire impedance spectrum. The ability to simulate TIS measurements allows rapid creation of impedance spectra for arbitrary thermal cell parameters. 

A thorough understanding of the microstructure of separators would be beneficial for modeling studies and optimization of electrochemical systems. This will help in making the battery model predictions more practical and reliable. The separator pore structure is usually very complex. It consists of a porous network of interconnected pores, which are filled with liquid electrolyte. A complete description of the pore structure would require a very intricate model. Simulations are only practically possible if a simplified quasi-continuum model involving a few parameters represents the strucmre. In such an approach, the effective electrolytic conductivity, Qgff, is often defined by [93]... 

Vasebi A, Partovibakhsh M, Bathaee SMT (2007) A novel combined battery model for state-of-charge estimation in lead-acid battraies based on extended Kalman filter for hybrid electric vehicle applications. J Power Sources 174 30-40. doi 10.1016/j.jpowsour.2007.04.011... 

In [23] an estimation routine is proposed for determining the model parameters. However, this method is not clearly reported. Thus, there is a need for well-defined methods for extraction of these parameters. Furthermore, the proposed methodology needs measuring the inside temperature of the battery for determining the other thermal battery model parameters. The inside battery temperature can be measured by inserting a thermal sensor in the battery, which carmot be done in real applications. 

In the proposed electrothermal model, an advanced electrical battery model is integrated, which has been developed based on statistical analysis on several lithium-ion batteries [42], The parameters of the electrical battery model can be extracted on the basis of the advanced Levenberg-Marquardt minimization tool [42]. 

As one can observe in Figure 11.15, the battery model shows a high accuracy vs. the experimental results the error is in the range of 0-0.7 °C. This indicates the high... 

In this chapter, an advanced lithinm-ion battery model is developed, which is able to predict the surface temperature Tg of the battery in different conditions. Here, a new methodology is proposed for determination of the thermal model parameters. 

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