Shriram Santhanagopalan

Theoretical Analysis of Stresses in a Lithium Ion Cell

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.

Parameter Estimation and Life Modeling of Lithium-Ion Cells

The lithium-ion cell is among the most popular candidates considered actively as a replacement for nickel-based batteries in automobile, small-electronics, satellite, and several other applications. This demand has fueled the need for improved performance and safety of the lithium-ion system. Consequently, a substantial amount of work has gone into understanding the mechanism of the capacity fade occurring in the battery experimentally and via rigorous theoretical analysis. 1-18

Battery Energy Storage System (BESS) and Battery Management System (BMS) for Grid-Scale Applications

The current electric grid is an inefficient system that wastes significant amounts of the electricity it produces because there is a disconnect between the amount of energy consumers require and the amount of energy produced from generation sources. Power plants typically produce more power than necessary to ensure adequate power quality. By taking advantage of energy storage within the grid, many of these inefficiencies can be removed. When using battery energy storage systems (BESS) for grid storage, advanced modeling is required to accurately monitor and control the storage system. A battery management system (BMS) controls how the storage system will be used and a BMS that utilizes advanced physics-based models will offer for much more robust operation of the storage system. The paper outlines the current state of the art for modeling in BMS and the advanced models required to fully utilize BMS for both lithium-ion batteries and vanadium redox-flow batteries. In addition, system architecture and how it can be useful in monitoring and control is discussed. A pathway for advancing BMS to better utilize BESS for grid-scale applications is outlined.

Parameter Estimation and Model Discrimination for a Lithium-Ion Cell

Two different models were used to obtain transport and kinetic parameters using nonlinear regression from experimental charge/ discharge curves of a lithium-ion cell measured at 35°C under four rates, C/5, C/2, 1C, and 2C, where the C rate is 1.656 A. The Levenberg-Marquardt method was used to estimate parameters in the models such as the diffusion of lithium ions in the positive electrode. A confidence interval for each parameter was also presented. The parameter values lie within their confidence intervals. The use of statistical weights to correct for the scatter in experimental data as well as to treat one set of data in preference to other is illustrated. An F-test was performed to discriminate between the goodness of fit obtained from the two models.

Optimal control and state estimation of lithium-ion batteries using reformulated models

First-principles models that incorporate all of the key physics that affect the internal states of a lithium-ion battery are in the form of coupled nonlinear PDEs. While these models are very accurate in terms of prediction capability, the models cannot be employed for on-line control and monitoring purposes due to the huge computational cost. A reformulated model [1] is capable of predicting the internal states of battery with a full simulation running in milliseconds without compromising on accuracy. This paper demonstrates the feasibility of using this reformulated model for control-relevant real-time applications. The reformulated model is used to compute optimal protocols for battery operations to demonstrate that the computational cost of each optimal control calculation is low enough to be completed within the sampling interval in model predictive control (MPC). Observability studies are then presented to confirm that this model can be used for state-estimation-based MPC. A moving horizon estimator (MHE) technique was implemented due to its ability to explicitly address constraints and nonlinear dynamics. The MHE uses the reformulated model to be computationally feasible in real time. The feature of reformulated model to be solved in real time opens up the possibility of incorporating detailed physics-based model in battery management systems (BMS) to design and implement better monitoring and control strategies.

Simulation of the Oxygen Reduction Reaction at an RDE in 0.5 M H 2 SO 4 Including an Adsorption Mechanism

Oxygen reduction on the surface of a rotating disk electrode RDE in 0.5 M H2SO4 is simulated by including mass transfer, adsorption, and charge transfer. A generalized model for the adsorption and reaction of several species is introduced. The oxygen reduction reaction is simulated as a limiting case where oxygen is the only species adsorbed, and oxygen reduction is the only reaction that takes place on the surface of the electrode. The model is based on the Nernst–Planck equations for mass transfer and the Butler–Volmer equation for electrochemical kinetics. The simulated polarization curves capture the change in the Tafel slopes, which are observed experimentally but cannot be explained by the normal four-electron-transfer mechanism. The adsorption model is compared with the four-electron-transfer model by fitting experimental data to both models using a nonlinear parameter estimation technique. The effects of changes in some important kinetic parameters are demonstrated. The oxygen reduction reaction ORR has been studied by using a rotating disk electrode RDE in acidic electrolytes such as sulfuric, perchloric, hydrochloric, and organic acid solutions. 1-4 Several reaction pathways have been proposed for the ORR based on the RDE experimental data, of which the four-electron pathway is primarily used to characterize the behavior of this reaction at a platinum electrode or a glassy carbon electrode coated with platinumbased catalyst. 5,6 The overall ORR is given by O2 +4 H + +4 e � 2H2O 1 where a mechanism that consists of four separate single-electrontransfer steps is implicitly assumed. A linear Tafel plot is expected for this four-electron reaction mechanism when the potential is lower than the standard electrode potential of 1.229 V vs the standard hydrogen electrode SHE. Note that all the potentials mentioned in this work are with respect to the SHE. The potential region of 1.0–0.6 V is where the polymer electrolyte membrane fuel cell PEMFC is operated practically. Important kinetic information such as the exchange current density and the transfer coefficient can be extracted by studying this voltage window for the ORR occurring at metal electrodes or carbonsupported platinum nanoparticle catalyst-coated electrodes. Transitions in the Tafel slopes for the ORR are observed when experimental data is analyzed. 2-4,7-11 The Tafel slope is just about doubled in the higher current density HCD region the potential region below about 0.8 V compared to the lower current density LCD region the potential region above 0.8 V. Table I presents a collection of examples from the literature which present changing Tafel slopes. When the temperature is around 298 K, the Tafel slope in the LCD region is around 60 mV/dec, which is close to 2.303RT/F, whereas this value is about 120 mV/dec or 2 2.303RT/F in the HCD region. The double Tafel slope phenomenon is observed at smooth surfaces such as electrodes made of polycrystalline Pt, Pt 111 ,P t100, or Pt alloy, etc., and at inert electrodes coated with nanosized carbon-supported Pt catalyst powder. 3 Various explanations have been suggested to explain the change in the Tafel slope, 12-17 and one of them is the oxygen adsorption mechanism, 14,16 which relates the change in the Tafel slope to the change in the applied potential. The adsorption of oxygen on the platinum surface is further complicated by the presence of other competing species and intermediates. 18,19 The adsorption of the anion HSO4 can compete with the molecular oxygen adsorption for the Pt site. 19 Reversible dissolution of water at the surface of the electrode can lead to PtOH formation in the potential region of 0.6–1.0 V vs SHE, and this process may interfere with the electrochemical reactions occurring at the surface of the electrode. 18 In this work, a generalized model is presented for the adsorption of multiple species Rl,sur. Each adsorbing species is assumed to be transported to the surface of the electrode and become adsorbed to the electrode surface to form Rl,ads Rl,sur Rl,ads

A Comparison of Numerical Solutions for the Fluid Motion Generated by a Rotating Disk Electrode

The velocity and pressure profiles in the electrolyte due to a rotating disk electrode are determined by solving the two-dimensional (2D) Navier-Stokes equations employing axial symmetry. Most applications in the literature employ a one-term approximation of the series solution to von Karmans one-dimensional (1D) model for the rotating disk electrode. In this work, the finite-element method is used to solve the model equations rigorously within an electrochemical cell of practical dimensions, and the results are compared with the one-term approximate solution and a complete solution to the ID model. The different hydrodynamic models are coupled with a mass-transport model for oxygen reduction reaction at the surface of the rotating ring disk electrode. The complete series solution is accurate to within four digits when compared to the 2D model, whereas the one-term approximation gives rise to an error as high as 4% in the limiting current values. Similar calculations on a ring disk electrode show that the one-term approximation underestimates the collection efficiency and the ratio of the ring and the disk currents of a sectioned electrode by 1-4%.

State of charge estimation for electrical vehicle batteries

Lithium ion batteries play an increasingly important role as high-rate transient power sources for hybrid electric vehicles, cycling around a relatively fixed state of charge (SOC). A crucial step in enhancing the performance of these batteries is the estimation of the state of charge as a function of the load. Most of the existing literature supports an empirical model - based on either an electric circuit, arbitrary pole placement or an analytical expression with an arbitrary set of parameters. Such empirical do not provide information on the physical limitations. Alternatively, an electrochemical cell model incorporating transport, kinetic and thermodynamic limitations can be used to estimate parameters that hold physical significance and hence provide a better insight into the cell performance. Estimating the SOC of a battery using physics-based models and filtering algorithms is illustrated. The relative merits and disadvantages of the approach are evaluated.

P-type doping of lithium peroxide with carbon sheets

The interaction of lithium peroxide (Li2O2) with carbon electrodes in Li-air batteries is studied with model systems of graphene-intercalated Li2O2, using density functional theory (DFT) methods. Although both the Li2O2 bulk and its stoichiometric surface structures (without single O atoms) are insulating, the incorporation of graphene sheets into the Li2O2 introduces hole states in the oxygen orbitals due to the electron transfer from the anti-bonding O2 orbitals to the graphene sheets. This indicates that carbon sheets not only provide conducting channels by themselves, but they also open new channels in Li2O2.

Using Piecewise Polynomials to Model Open-Circuit Potential Data

Curve fitting is commonly used to determine a mathematical expression for sets of experimental data. While there are many instances when theory dictates a linear, quadratic, or other simple mathematical form for a relationship, there are often times when the theoretical form is either unknown or too unwieldy to be used effectively. A common example is the open-circuit-potential relationship of a Li-ion battery. One may use empirical correlations such as high-order polynomials (HOP) or various types of splines which are piecewise polynomials of low order. Despite their simplicity, HOPs are often undesirable given their numerical instability as well as their poor extrapolation performance. Certain splines generally produce acceptably smooth curves but use an unacceptably large number of fitting parameters. A method is presented for construction of continuous and smooth piecewise polynomials. Using significantly fewer polynomial segments than experimental data points, the number of parameters required to develop the calibration curves of a Li-ion battery is substantially reduced from that of splines while maintaining a similar level of fit quality. Mixed-integer programming techniques are employed to ensure that the knot (transition point) placement is optimal.