The single-particle model presented by Santhanagopalan et al. ͓J. Power Sources, 156, 620 ͑2006͔͒ is extended to include an energy balance. The temperature dependence of the solid phase diffusion coefficient of the lithium in the intercalation particles, the electrochemical reaction rate constants, and the open circuit potentials ͑OCPs͒ of the positive and negative electrodes are included in the model. The solution phase polarization is approximated using a nonlinear resistance, which is a function of current and temperature. The model is used to predict the temperature and voltage profiles in a lithium-ion cell during galvanostatic operations. The single-particle thermal model is validated by comparing the simulated voltage and temperature profiles to the results obtained using a distributed porous electrode model. The simulation results from the single-particle thermal model also show good agreement with experimental voltage data obtained from lithium-ion pouch cells under different discharge rates ͑C/33, C/2 and C͒ at different temperatures ͑15, 25, 35, and 45°C͒.

A thermal model for a lithium-ion cell is presented and used to predict discharge performance at different operating temperatures. The results from the simulations are compared to experimental data obtained from lithium-ion pouch cells. The model includes a set of parameters ͑and their concentration and temperature dependencies͒ that has been obtained for a lithium-ion cell composed of a mesocarbon microbead anode, LiCoO 2 cathode in 1 M LiPF 6 salt, in a mixture of ethylene carbonate, propylene carbonate, ethyl-methyl carbonate, and diethyl carbonate electrolyte. The parameter set was obtained by comparing the model predictions to the experimental discharge profiles obtained at various temperatures and rates. The concentration and temperature dependence of the extracted parameters were correlated through empirical expressions. Also, the effect of including the thermal dependence of various parameters in the model on the simulated discharge profiles is discussed.

A mathematical model to simulate the generation of mechanical stress during the discharge process in a dual porous insertion electrode cell sandwich comprised of lithium cobalt oxide and carbon is presented. The model attributes stress buildup within intercalation electrodes to two different aspects: changes in the lattice volume due to intercalation and phase transformation during the charge/discharge process. The model is used to predict the influence of cell design parameters such as thickness, porosity, and particle size of the electrodes on the magnitude of stress generation. The model developed in this study can be used to understand the mechanical degradation in a porous electrode during an intercalation/deintercalation process, and the use of this model results in an improved design for battery electrodes that are mechanically durable over an extended period of operation.

A mathematical model is presented to predict the performance of a lithium-ion battery. It includes the changes in the porosity of the material due to the reversible intercalation processes and the irreversible parasitic reaction. The model was also extended to predict the capacity fade in a lithium-ion battery based on the unwanted parasitic reaction that consumes Li ϩ along with the changes in the porosities of the electrodes with cycling due to the continuous parasitic side reaction. The model can be used to predict the drop in the voltage profile, change in the state of charge, and the effects of charge and discharge rates during cycling.

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An analytical expression for the impedance response of an insertion cathode/separator/foil anode cell sandwich is presented. The analytical expression includes the impedance contributions from interfacial kinetics, double-layer adsorption, and solution-phase and solid-phase diffusion processes. The validity of the analytical solution is ascertained by comparison with the numerical solution obtained for a LiCoO 2 /polypropylene/lithium metal cell. The flexibility of the analytical solution is utilized to analyze various limiting conditions. An expression to estimate solid-phase diffusion coefficient of insertion species in a porous electrode influenced by the solution-phase diffusion process is also derived. Electrochemical impedance spectroscopy ͑EIS͒ technique has been extensively used in the analysis of lithium battery systems, especially to determine kinetic and transport parameters, 1-3 understand reaction mechanisms, 4 and to study degradation effects. [5][6][7] However, the mathematical interpretation of the impedance response of electrochemical systems is complicated by the processes occurring in the system. This drives researchers to adopt lumped circuit models [8][9][10] or finite transmission line models 11 to interpret impedance data. However, these types of models provide little information on the fundamental physical processes occurring in the cell. To gain more understanding of the physical processes, macrohomogenous models for porous electrodes have been used by some researchers. [12][13][14][15][16][17][18] These models primarily use porous electrode theory 19,20 to describe the porous nature of the electrode/separator and concentration solution theory to treat the transport processes in the electrolyte phase. The thermodynamics and kinetics of the reactions at the electrode/electrolyte interface are also described in these models in detail. Most of these models also account for the solidphase diffusion of the active species into the bulk. While such detailed models throw light on the impedance behavior of systems when complicated by transport and kinetic processes, the mathematical interpretation is not straightforward.In the list of comprehensive models developed to simulate the impedance behavior of lithium batteries, Doyle et al. 13 simulated the impedance response for a metal anode/separator/porous cathode system with all the above-mentioned details. Guo et al. 15 used a similar model to estimate the diffusion coefficient of lithium in carbon. Later, Dees et al. 18 included an electronically insulating oxide layer at the electrode/electrolyte interface to model a LiNi 0.8 Co 0.15 Al 0.05 O 2 cathode. However, these models use a numerical scheme to solve for the variables to obtain the frequency domain impedance spectrum. There are also some analytical models 14,16,17 available in the literature, but they are not as comprehensive as the numerical models. Meyers et al.14 presented an analytical solution to the impedance response of a porous electrode in the absence of solution-phase concentr...

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A one-dimensional model for predicting the performance of a battery/electrochemical capacitor-hybrid system has been developed. Simulation results are presented for a LiCoO 2 ͉LiPF 6 ethylene carbonate/dimethyl carbonate͉carbon battery system and a Maxwell PC 10F carbon double-layer electrochemical capacitor. The current shared between the battery and the electrochemical capacitor at very short times depends on the ohmic resistances of the battery and the capacitor. As the discharge proceeds, the operating conditions such as frequency, duty ratio, and peak pulse discharge current control the current shared among parallel circuits. These parameters also determine the extent of the run time increase of the hybrid system as compared to the battery system. The inclusion of a number of identical series/parallel capacitors is considered in the present model by introducing the parameter, capacitor configuration index. Ragone plots are simulated for a battery-alone and a hybrid system. A substantial improvement in the available energy density is observed while operating hybrid systems under high power densities. Finally, a general optimization approach is presented. Electrochemical double-layer capacitors are the most suitable power source for high-powered applications such as electric vehicles, power distribution systems, uninterrupted power supply, hybrid vehicles and other electronic devices due to their high power densities.1,2 However, their energy densities are considerably lower than those of high-energy battery systems such as lithium ion. Although advanced battery systems and double-layer electrochemical capacitors contrast with regard to energy-power relationship, in combination they can be utilized as an effective power source. In several experimental studies, hybrid systems with batteries and capacitors have been demonstrated to extend the run time and improve the power capability of the battery.3,4 However, there has not yet been a rigorous theoretical analysis on this subject. Dougal et al. 5 presented analytical solutions to a simplified model of a batterycapacitor hybrid system based on circuit modeling and discussed in detail the energy efficiency, power capabilities, and current sharing between the battery and the capacitor. However, a more systematic study on an electrochemical basis is required to understand the processes occurring in the battery-capacitor hybrid system in order to evaluate and improve the performance.The objective of this paper is to develop a more sophisticated macrohomogenous model to simulate the performance of a batteryelectrochemical capacitor hybrid system and to analyze the improvement in performance compared to that of battery-alone systems under high-current pulse loads. Pulse loads were typically chosen because they are frequently encountered in portable power systems such as machine guns, implantable cardioverter defribillators, electric vehicles and in wireless telecommunication systems. The model addresses the effect of pulse operating conditions, specifically the duty ...