Pseudo Two-dimensional Model Research Articles

Ion cell performance using single particle representation of battery electrode

The aim of study is to predict the performance of lithium-ion cells using the single particle representation of battery electrode model. The model is developed starting from the concentration solution theory and porous-electrode formulation, with Fick's law governing the diffusion of ions in the solid electrode. Since the solution of the governing equations is difficult due to their non-linear nature, simplifying assumptions are made that considerably reduce the computational time needed to predict cell performance. The model is then used to determine the concentration of lithium in solid phase and the electrode potential, assuming that the lithium concentration remains fixed in electrolyte. Further this model is compared with the pseudo two-dimensional model to simulate cyclic performance of lithium-ion cells under various operating conditions.

Optimal Health-aware Charging Protocol for Lithium-ion Batteries: A Fast Model Predictive Control Approach

Lithium-ion batteries are widely used in industry to supply different portable applications. Their management is handled by Battery Management Systems (BMSs), which are intended to ensure good performance (such as minimum charging time) while simultaneously minimizing safety risks. The use of accurate mathematical models can help in achieving such goals. The first-principles pseudo-two dimensional (P2D) model is one of the mostly used models for simulation but rarely used in design of BMSs. This model, together with a description of the capacity fade mechanisms occurring during battery operations, is used to design health-aware BMS strategies. A Model Predictive Control (MPC) scheme based on a linearized version of the P2D model is proposed in order to track a reference value of the State of Charge (SOC), while taking into account the aging dynamics of the system as well as temperature and voltage constraints. Simulations show the effectiveness of the approach: the tuning of the control parameters allows controlled operation with different tradeoffs between charging time and battery lifetime enhancement.

A Porous Electrode Model for the Magnesiation and Demagnesiation of a Bismuth Electrode in Rechargeable Magnesium-Ion Cells

The transport and electrochemical properties of magnesium ions (Mg2+) in a magnesium organohaloaluminate electrolyte were estimated experimentally. The key properties of a Bismuth (Bi) electrode; such as solid-state Mg2+ diffusion, electronic conductivity, particle size, and electrode porosity were also estimated, both experimentally and theoretically. The magnesium organohaloaluminate electrolyte was utilized in an electrochemical cell to study the Mg2+ insertion/extraction reactions in a Bi electrode. The existing porous electrode pseudo two-dimensional model was extended in the proposed study to describe the behavior of the α-Mg3Bi2/Mg cell system during charge-discharge reactions. The model was also modified to include experimentally evaluated parameters such as internal resistance, electrode kinetics, thermodynamics, and the diffusion of Mg2+ in the active particles. This electrochemical model, modified with estimated parameters for the electrolyte, Mg, and α-Mg3Bi2 electrodes, was formulated with both, direct 2-electron transfer and multi-electron transfer from each magnesium atom of the magnesium dimer present in the electrolyte. Details of the electrochemical performance from both mechanisms are compared with the experimental data, and factors governing the performance of the α-Mg3Bi2/Mg cell are discussed in the present study.

Three-dimensional Multi-Particle Electrochemical Model of LiFePO4 Cells based on a Resistor Network Methodology

An efficient fundamental approach for three-dimensional modeling of LiFePO4 (LFP) battery pouch cells is presented in this paper. First, the standard Newman pseudo two-dimensional (P2D) model is compared with two simplified approaches developed by the authors: a simplified electrochemical multi-particle (SEMP) model, and a homogenous pseudo two-dimensional (HP2D) model. It is shown that the SEMP and HP2D models can predict the operating voltage of LFP half-cells with less than 2.5% and 1.5% maximum error, respectively, when compared to the P2D model. It is also shown that the simulation time of these two simplified models are one order of magnitude less than the P2D model, hence, they are then used for three-dimensional modeling of the LFP half-cell. Multiple one-dimensional SEMP models are combined, as a first approach, to form a three-dimensional battery model. It is explained that although this method is adequate for predicting the electrochemical current generation distribution, it may introduce errors in heat generation calculations since it does not consider the electrolyte concentration and potential gradient parallel to the current collectors. Therefore, using the HP2D model, an optimized method is proposed that combines the speed and simplicity of the first approach with three-dimensional simulation of the electrolyte. It is shown that this method is able to predict the mentioned gradients that contribute to the battery heat generation.

Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter

This paper investigates the state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200 s despite a 30% error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.

A pseudo 2-D surface potential model of a dual material double gate junctionless field effect transistor

In this paper, we have developed a pseudo two-dimensional (2-D) analytical model for the surface potential of a dual-material double-gate junctionless field-effect transistor. We have incorporated the effects of depletion into the source and drain regions to model the surface potential for all three operating modes: (a) full depletion, (b) partial depletion, and (c) near flatband. The effects of the device parameters such as oxide thickness, silicon thickness, and impurity concentration on the surface potential is demonstrated through the model. The model is further extended to derive an expression for the threshold voltage which predicts the expected change with respect to variation in the device parameters. The accuracy of the proposed model is verified against 2-D numerical simulations.

Li-Ion Battery State Estimation Using a Pseudo Two-Dimensional Electrochemical Model-Based Extended Kalman Filter with Temperature and Degradation Effects

We discuss the estimation of lithium-ion battery states using an extended Kalman filter based on the Doyle, Fuller and Newman pseudo two-dimensional (P2D) electrochemical model [1]. The P2D model is solved using our computationally efficient Matlab implementation [2] that uses Chebyshev orthogonal collocation. In order to predict the cell capacity and power fade, the P2D model is coupled to a bulk thermal model and a degradation model describing the formation of the solid-electrolyte interphase (SEI) [3]. This state estimation algorithm could be used online for advanced battery management systems (BMS) for electric vehicles and other applications. BMSs are embedded systems that monitor and control individual cells of a battery pack to ensure safe and optimal energy use. The estimation of battery states such as state-of-charge (SOC), state-of-health (SOH) and instantaneous power capability is an important function fulfilled by the BMS, requiring measurements of current, voltage and temperature combined with an accurate battery model. Current approaches usually employ low-order equivalent circuit models (ECMs) due to their low computational requirements. However, these are only accurate within a narrow operating range, and accounting for changes in dynamics and performance caused by degradation is difficult due to the lack of physical meaning of model parameters. Battery models such as the P2D model [1] are based on equations of conservation and are accurate over a wider operating range accounting for various effects, including temperature and degradation. However, these are usually too computationally intense for embedded applications. Instead, we focus on efficient numerical methods called spectral methods that have been recently applied by us and others to the P2D model to reduce the computational burden while maintaining accuracy [2, 4, 5]. We have also recently demonstrated this method applied to super-capacitor modeling [6]. We have implemented an efficient solution of the P2D model coupled to a bulk thermal model, with temperature- and concentration-dependent parameters, using the orthogonal collocation on Chebyshev polynomials spectral method to spatially discretize the partial differential equations of the model. This reduces the order of the discretized model by a factor of 100-1000 compared to finite difference or finite element methods whilst maintaining a similar accuracy. Figure 1 shows the voltage predicted using the spectral method (markers) compared to a finite element solution using Comsol (solid-lines), both are in very good agreement to high C-rates, and the solution time is 50-100 times faster with spectral methods. Modelling degradation is of utmost importance for automotive applications in order to estimate and predict the capacity and power fade of cells. The loss of lithium and the increase of battery impedance due to the formation and growth of the solid-electrolyte interphase (SEI) are believed to be the major degradation mechanisms in commercial graphite anode-based cells. We coupled our efficient implementation of the thermal-P2D model to a degradation model describing the evolution of the SEI layer thickness [3, 7]. The coupled thermal-P2D and degradation model is efficiently solved in Matlab using a unified control-engineering state space approach. Several techniques are available for the state estimation of such a non-linear state-space model, including the extended Kalman filter (EKF), the unscented Kalman filter (UKF) or moving horizon estimation (MHE). Although the UKF and MHE may provide a more accurate estimation, these are computationally intensive. Instead, we focus on a modified EKF that shows satisfactory performance with lower computational resources requirements. The state estimation algorithm is able to estimate the concentration profiles within the cell and the SEI growth during the cell operation. Due to its relatively low computational requirements, our state estimation algorithm could be solved online in a BMS to accurately monitor and predict SOC, SOH and instantaneous power capability. Acknowledgements This work is funded by Samsung Electronics Co. Ltd. through a Global Research Outreach award.

Using Pseudo-Two-Dimensional (P2D) Reformulation Model with a Particle Filter to Estimate State of Charge, State of Health, and Remaining Useful Life in Li-Ion Battery Management System (BMS)

Discovering the precise state of charge (SOC), state of health (SOH), and remaining useful life (RUL) while monitoring depth of discharge (DOD) for Lithium ion (Li-ion) batteries can be computational enormous. Electrical engineers using equivalent circuit models (ECM) or enhanced equivalent circuit models (EECM) have achieved an acceptable level of accuracy modelling the current, voltage, and temperature behaviors to get SOC, SOH, RUL, and DOD. ECMs and EECMs are computationally fast but do not fully account for the electrochemical material that makes up the battery in their mathematical equations or isothermal characteristics that continuously change during charging and discharging. Chemical engineers have achieved greater levels of accuracy using physical-based models over ECMs and EECMs. Unfortunately, the number of factors and variables needed to compute the system of differential algebraic equations for the nonlinear physical-based models to achieve this level of precise data is computationally too expensive for real-time systems. In today’s environment, the use of filters has provided a bridge between empirical and physical based models. This paper examines an ECM and a porous electrode pseudo two-dimensional (P2D) model using particle filter (PF) technology for a series, parallel, and series/parallel combination battery switching microcontroller based battery management system (BMS). Mathematical and Physical Models BMSs are developed to manage the charging and discharging profile, and basic knowledge of all the states that the battery topology goes through is paramount in order to design a safe and more sustainable battery system. ECMs are used in BMSs because they can model battery characteristics for a desired state using resistors and capacitors to emulate the internal battery cell resistance and capacitance behaviors. Because ECMs are linearly based mathematical equations, simulation of these models can be performed quickly. Additionally, Kalman filtering techniques (KFT) have been used extensively with ECMs to assist in the estimation of the SOC and SOH for BMSs. However, the effectiveness of ECMs and KFTs are not optimal for the non-linear behavior of batteries. Physical based models have the advantage of performing comprehensive analysis on the effects of both the solid phase and the liquid phase, but they can be computationally complex. Modelling, porous electrode theory coupled with transport phenomena, and electrochemical reactions represented by coupled nonlinear partial differential equations in one or two dimensions give physical based models an advantage over ECMs. Santhanagopalan [1] and Rahimian [2] have used the single particle model (SPM) implementing Kalman filtering methods to estimate SOC of Li-ion cells. Efforts by Subramanian et al. [3] focused on a physical based P2D reformulated model characterized by solid-electrolyte interface layer growth, constant current–constant voltage, and capacity fade as it related to battery degradation to determine the manner in which extreme temperature and high charging rates affect the battery “calendar life.” This paper will simulate a reformulated P2D SOC and SOH convergence based model using the governing equations of a SPM with lithium active particles as in Northrop [4]: Eq (1), Eq (2), Eq (3) Particle Filter Methodology The PF is an algorithm based on a recursive Monte Carlo technique of estimating the posterior density of the state variable given a set of observation variables. The sequential importance sampling (SIS) algorithm implements the recursive Bayesian filter by associating weights to random samples representing the required posterior density. The sequential importance resampling (SIR) filter adapts the SIS features and adds a resampling phase. The posterior PDF approximation can be defined as in [5]: Eq (4), Eq (5) Results Figure 1(a) shows the simulated discharge (at 1C rate) of a 1.2 Volt Li-ion battery at 100% SOC using an empirical ECM in MatLab Simulink. Figure 1(b) includes simulated measured (noisy), SIS, and SIR filtered battery discharge data. Figure 1 Battery Voltage Profile Future work will include a reformulated physical based P2D PF battery model to simulate SOC, SOH, and RUL of a BMS. References Santhanagopalan, Shriram, et al. "Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries." JPS 156.2 (2006): 620-8. Print. Rahimian, S.K., S. Rayman, and R.E. White. “State of Charge and Loss of Active Material Estimation of a Lithium Ion Cell under Low Earth Orbit Condition Using Kalman Filtering Approaches.” ECS (2014): A860-A872. Subramanian, Venkat R., et al. "Mathematical Model Reformulation for Lithium-Ion Battery Simulations: Galvanostatic Boundary Conditions." ECS 156.4 (2009): A260-71. Print.Northrop, Paul W. C., et al. "Efficient Simulation and Reformulation of Lithium-Ion Battery Models for Enabling Electric Transportation." ECS 161.8 (2014): E3149-57. Print.Arulampalam, M. S., et al. "A Tutorial on Particle Filters for Online nonlinear/non-Gaussian Bayesian Tracking." Signal Processing, IEEE Transactions on 50.2 (2002): 174-88. Print. Figure 1

Living cardiac tissue slices: An organotypic pseudo two-dimensional model for cardiac biophysics research

Living cardiac tissue slices, a pseudo two-dimensional (2D) preparation, have received less attention than isolated single cells, cell cultures, or Langendorff-perfused hearts in cardiac biophysics research. This is, in part, due to difficulties associated with sectioning cardiac tissue to obtain live slices. With moderate complexity, native cell-types, and well-preserved cell–cell electrical and mechanical interconnections, cardiac tissue slices have several advantages for studying cardiac electrophysiology. The trans-membrane potential (Vm) has, thus far, mainly been explored using multi-electrode arrays. Here, we combine tissue slices with optical mapping to monitor Vm and intracellular Ca2+ concentration ([Ca2+]i). This combination opens up the possibility of studying the effects of experimental interventions upon action potential (AP) and calcium transient (CaT) dynamics in 2D, and with relatively high spatio-temporal resolution.As an intervention, we conducted proof-of-principle application of stretch. Mechanical stimulation of cardiac preparations is well-established for membrane patches, single cells and whole heart preparations. For cardiac tissue slices, it is possible to apply stretch perpendicular or parallel to the dominant orientation of cells, while keeping the preparation in a constant focal plane for fluorescent imaging of in-slice functional dynamics. Slice-to-slice comparison furthermore allows one to assess transmural differences in ventricular tissue responses to mechanical challenges. We developed and tested application of axial stretch to cardiac tissue slices, using a manually-controlled stretching device, and recorded Vm and [Ca2+]i by optical mapping before, during, and after application of stretch.Living cardiac tissue slices, exposed to axial stretch, show an initial shortening in both AP and CaT duration upon stretch application, followed in most cases by a gradual prolongation of AP and CaT duration during stretch maintained for up to 50 min. After release of sustained stretch, AP duration (APD) and CaT duration reverted to shorter values.Living cardiac tissue slices are a promising experimental model for the study of cardiac mechano-electric interactions. The methodology described here can be refined to achieve more accurate control over stretch amplitude and timing (e.g. using a computer-controlled motorised stage, or by synchronising electrical and mechanical events) and through monitoring of regional tissue deformation (e.g. by adding motion tracking).

Model Reformulation for Coupled Electrochemical-Mechanical Pseudo Two-Dimensional Model

Rechargeable lithium-ion batteries have been extensively used in mobile communication and portable instruments due to their high volumetric and gravimetric energy density and low self-discharge rate, leading many scientists and engineers to work towards developing lithium-ion batteries with improved performance and longer life.The porous electrode pseudo two-dimensional (P2D) model is popular in the literature for simulating lithium-ion battery performance.(1) This model has proven versatile enough to be expanded as understanding of the battery system is improved.(2-7) However, the computationally expensive nature of the model has led to the development of reformulated and reduced order models to improve the computational efficiency of simulation.(8-13) The P2D model has proven to accurately simulate single charge-discharge cycles, but the base model does not consider capacity fade mechanisms which are important for life evolution of the system. One source of degradation of lithium-ion batteries is the stress caused by intercalation and deintercalation of lithium into the solid active material.(14-17) Several models have been developed to calculate intercalation induced stresses of varying levels of complexity.(15, 17-21) The stress generated within the particle affects the concentration profile and cannot be captured solely by simple Fickian diffusion. Therefore, pressure induced diffusion must be included when solving for solid phase diffusion in the pseudo radial dimension r within the particle and can affect behavior at high rates of charge. Previously, the effects of stress and pressure induced diffusion have been incorporated into the single particle (SP) model using a mixed finite difference approach to discretize the solid phase concentration.(22)Here we expand the P2D model to study the generation of stresses within the active material of a lithium-ion cell. Unlike the SP model, the P2D model allows the variation in stress to be modeled across the thickness of the electrode and is also valid for higher rates of operation. Coupling the stress-strain models with the P2D model allows better analysis of the maximum stress that occurs in the system to determine what operating conditions lead to undesirable stress generation. Reformulation in the pseudo dimension, r, based on the work by De, et al.(22) will be combined with reformulation in the primary dimension, x, based on the work by Northrop, et al.(13) in order to reduce the computational cost considerably so that control and optimization can be performed with consideration to the stress development within the cell. Better understanding can lead to better control and operation to improve the overall life of the battery, especially in high power applications. Acknowledgements The authors acknowledge financial support by the National Science Foundation under grant numbers CBET-0828002, CBET-0828123, and CBET-1008692, and the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275.

Pseudo 2D chemical model of hot-Jupiter atmospheres: application to HD 209458b and HD 189733b

We have developed a pseudo two-dimensional model of a planetary atmosphere, which takes into account thermochemical kinetics, photochemistry, vertical mixing, and horizontal transport, the latter being modeled as a uniform zonal wind. We have applied the model to the atmospheres of the hot Jupiters HD 209458b and HD 189733b. The adopted eddy diffusion coefficients are calculated by following the behaviour of passive tracers in three-dimensional general circulation models, which results in eddy values significantly below previous estimates. We find that the distribution of molecules with altitude and longitude in the atmospheres of these two hot Jupiters is complex because of the interplay of the various physical and chemical processes at work. Much of the distribution of molecules is driven by the strong zonal wind and the limited extent of vertical transport, resulting in an important homogenisation of the chemical composition with longitude. In general, molecular abundances are quenched horizontally to values typical of the hottest dayside regions, and thus the composition in the cooler nightside regions is highly contaminated by that of warmer dayside regions. As a consequence, the abundance of methane remains low, even below the predictions of previous one-dimensional models, which is likely to be in conflict with the high CH4 content inferred from observations of the dayside of HD 209458b. Another consequence of the important longitudinal homogenisation of the abundances is that the variability of the chemical composition has little effect on the way the emission spectrum is modified with phase and on the changes in the transmission spectrum from the transit ingress to the egress, these variations in the spectra being mainly due to changes in the temperature rather than in the composition between the different sides of the planet.

Shale Gas Pseudo Two-Dimensional Unsteady Seepage Pressure Simulation Analysis in Capillary Model

Shale gas is rapidly growing as a source of natural gas in China. Compared with the conventional gas reservoir, the shale gas reservoir is characterized by low porosity, low permeability, and adsorbed gas, making the flow mechanism of shale gas reservoir more complex. In this study, we investigated six factors influencing the gas flow: the Darcy flow, the slippage effect, the Knudsen diffusion effect, the desorption of gas on pore walls, the diffusion effect of gas in organic matter, and the matrix deformation effect. We simplified gas flow in the development process to only include gas flow in the capillaries and then considered the six influence factors. This study establishes a shale gas pseudo two-dimensional unsteady capillary seepage mathematical model based on the continuity equation, using the implicit difference method to solve the mathematical model. Certain capillary parameters were added to the calculation, and the study analyzed the effect of the different factors on both the pressure distribution and the cumulative gas production. Results show that the Knudsen diffusion effect and the desorption of gas from pore walls have lower impact on the pressure than the others factors. The diffusion effect of gas in organic matter, the slippage effect, and the matrix deformation effect have a stronger impact on the pressure. The gas in organic matter continuously diffuses into the capillary with the increasing of the production time, and the pressure drop becomes slow because of the gas diffusion.

State of Charge Estimation in Li-ion Batteries Using an Isothermal Pseudo Two-Dimensional Model

The dynamics of Li-ion batteries are often defined by a set of coupled nonlinear partial differential equations called the pseudo two-dimensional model. It is widely accepted that this model, while accurate, is too complex for estimation and control. As such, the literature is replete with numerous approximations of this model. For the first time, an algorithm for state-of-charge estimation using the original pseudo two-dimensional model is provided. A discrete version of the model is reformulated into a state-space model by separating linear, nonlinear, and algebraic states. This model is high dimensional (of the order of tens to hundreds of states) and consists of implicit nonlinear algebraic equations. The degeneracy problems with high-dimensional state estimation are circumvented by developing a particle filter algorithm that sweeps in time and spatial coordinates independently. The implicit algebraic equations are handled by ensuring the presence of a ‘tether’ particle in the algorithm. The approach is illustrated through simulations.

Multiphysics modeling of lithium ion battery capacity fading process with solid-electrolyte interphase growth by elementary reaction kinetics

A pseudo two-dimensional mathematical model is developed for a lithium ion battery, integrating the elementary reaction based solid-electrolyte interphase (SEI) growth model with multiple transport processes. The model is validated using the experimental data. Simulation results indicate that the operating temperature has great effect on the SEI layer generation and growth. Under different charging–discharging rates, it is found that high charging–discharging rate can intensify the battery capacity fading process. Different cooling conditions are then applied and show that enhanced surface convective cooling condition can effectively slow down the battery capacity fading. After that, the effect of electrolyte salt concentration and exchange current density are studied. It is found that raising the electrolyte salt concentration can improve the diffusion property of lithium ions, and stabilize the battery performance under lithium ion consumption induced resistance rising. It also suggests that improving exchange current density could greatly decrease the lithium ion battery capacity fading.

Lithium ion cell modeling using orthogonal collocation on finite elements

The physics-based pseudo two-dimensional (P2D) model for lithium ion cells requires significant computation time. To reduce this burden, the orthogonal collocation on finite elements (OCFE) method is applied here. The number of node points both in the macro-scale and in the micro-scale in the P2D model is reduced by optimally locating the node points. This OCFE method is shown to be better than other approximate methods for the spherical diffusion equation with flux boundary conditions. This OCFE method is also used to solve the P2D model equations and the results are compared to those obtained from COMSOL (a commercial differential/algebraic equation solver using FEM).

On the High Rate Capability of LiFePO4

A pseudo two-dimensional macro-homogeneous model has been used to understand the high-rate capability of LiFePO4. The circumstances that can facilitate the fast and ultra-fast rate behavior of this material are identified and discussed in detail. For the electrode designs used in the studies, it was found that the solid-phase mass transport rate has a significant effect on the rate capability of LiFePO4. The size distribution of the LiFePO4 particles has an effect on the high rate charge and discharge behavior of the material. These and other consequences are discussed using experimental data and model predictions.

The geometry and motion of nematode sperm cells

The nematode sperm cell crawls by recycling major sperm protein (MSP) from dimers into subfilaments, filaments, and filament complexes, as a result of thermal writhing in the presence of hydrophobic patches. Polymerization near leading edges of the cell intercolates MSP dimers onto the tips of growing filament complexes, forcing them against the cell boundary, and extending the cytoskeleton in the direction of motion. Strong adhesive forces attach the cell to the substrate in the forward part of the lamellipod, while depolymerization in the rearward part of the cell breaks down the cytoskeleton, contracting the lamellipod and pulling the cell body forward. The movement of these cells, then, is caused by coordinated protrusive, adhesive and contractile forces, spatially separated across the lamellipod. This paper considers a phenomenological model that tracks discrete elements of the cytoskeleton in curvilinear coordinates. The pseudo-two dimensional model primarily considers protrusion and rotation of the cell, along with the evolution of the cell boundary. General assumptions are that pH levels within the lamellipod regulate protrusion, contraction and adhesion, and that growth of the cytoskeleton, over time, is perpendicular to the evolving cell boundary. The model follows the growth and contraction of a discrete number of MSP fiber complexes, since they appear to be the principle contributors for force generation in cell boundary protrusion and contraction, and the backbone for the dynamic geometry and motion.

Toward Real-Time Simulation of Physics Based Lithium-Ion Battery Models

Recent interest in lithium-ion batteries for electric and hybrid vehicles, satellite, defense, and military applications has increased the demand on the computational efficiency of lithium-ion battery models. This paper presents an effective approach to simulate physics based lithium-ion battery models in real-time (milliseconds) for simulation and control in hybrid environments. The battery model used for the simulation is derived from the first principles as an isothermal pseudo two-dimensional model with incorporation of concentrated solution theory, porous electrode theory, and due consideration for the variations in electronic/ionic conductivities and diffusivities using the Bruggmann coefficient.

Suppression of the cardiac electric field artifact from the heart action evoked potential

The study of heart action-related brain potentials is strongly disrupted by the presence of an inherent cardiac electric artifact. The hypothesis is presented that most of the electric current coupled to the cardiac field surrounds the skull and flows through the scalp tissue without crossing the cranial cavity. This pseudo two-dimensional conduction model contrasts with the volumetric conduction of the brain electrical activity, and this property is exploited to cancel the cardiac electric artifact. QRS loop vector-cardiographic projections on saggital planes were recorded in 11 healthy subjects in the head and neck areas. Comparative analysis of the projection eccentricities, estimated by the correlation coefficients of the paired data on each area, supported the hypothesis and allowed the handling of the cardiac electric field at the scalp as if enclosed in a two-dimensional wrapped space. This approach permitted the combination of different heart action-related brain potentials recorded at different electrode positions to cancel the cardiac electric artifact. The cancellation method, applied to the subjects' EEG data, yielded a slow cortical potential with a negligible cardiac electric residue and an amplitude of about 1.5-2 microV, with a maximum around 150 ms and a minimum at 400 ms post-R wave.

Review of models for predicting the cycling performance of lithium ion batteries

A rigorous pseudo two-dimensional model to simulate the cycling performance of a lithium ion cell is compared with two simplified models. The advantage of using simplified models is illustrated and their limitations are discussed. It is shown that for 1 C or less discharge rates a simple ordinary differential equation (ODE) model can be used to predict accurately the potential as a function of time. For rates higher than 1 C, simplifications to the rigorous model are suggested that reduce the solution time for the model.