Lithium-ion Cell Model Research Articles

An extended single particle model-based parameter identification scheme for lithium-ion cells

The accurate modeling and parameter identification of lithium-ion battery are of great significance in real-time control and high-performance operation for advanced battery management system (BMS) in electrified vehicles (EVs). However, it is difficult to obtain the information about the interior state inside battery, because it cannot be directly measured by some electric devices. In order to accurately identify the key state parameters of lithium-ion cell applied to electric ground vehicles, an extended single particle model of lithium-ion cell with electrolyte dynamics behaviors is first built up based on the porous electrode theory and concentration theory in this article. Compared with the conventional single particle cell model, the parameter description of the solid electrolyte interface film is incorporated into this model, and the coupled effects of temperature-dependent and electrolyte-dependent electrochemical parameters on the cell discharge are also taken into consideration. Based on this extended single particle cell model, a simplified parameter sensitivity analysis method and a comprehensive parameter identification scheme for lithium-ion cell are proposed herein, in which a sensitivity analysis of the capacity to a subset of electrochemical parameters that are hypothesized to evolve throughout the battery's life, is conducted to determine the highly sensitive parameters to be identified under some particular operation scenarios, and further to solve the parameter optimization problem using the genetic algorithm. Based on this method, the test data under the working condition of 1 C discharge rate at 23℃ are employed to evaluate the identified parameters of lithium-ion battery cell with a peak value of voltage error less than 3.8%. Afterwards, the effectiveness and feasibility of the proposed parameter identification scheme are validated by the comparative study of the simulated output voltage and the experimental output voltage under the same input current profile. Specifically, the 0.05 C discharge and HPPC (hybrid pulse power characterization) current profile are used to verify the evaluated parameters under the 1 C discharge condition, and the maximum relative errors of voltage with 0.05 C galvanostatic discharge profile at 23 and 45℃ are 3.4% and 2.6% by using our proposed SPMe_SEI model, and 5.7% and 4.0% by using the traditional SPMe model, respectively. Moreover, the maximum relative errors of voltage with HPPC discharge profile at 23 and 45℃ are 1.9% and 1.5% by using our proposed SPMe_SEI model, and 2.1% and 1.8% by using the traditional SPMe model, respectively. It is concluded that the proposed parameter identification scheme for a lithium-ion cell model can provide a solid theory foundation for facilitating the estimation of state-of-health in BMS application.

Complete cell-level lithium-ion electrical ECM model for different chemistries (NMC, LFP, LTO) and temperatures (−5 °C to 45 °C) – Optimized modelling techniques

In this study a complete cell-level electrical equivalent circuit model (ECM) of energy and power lithium-ion cells with 3 different chemistries and multiple temperatures (−5 °C to 45 °C) is developed and validated under different dynamic load profiles. The chemistries under investigation are Nickel Manganese Cobalt 20 Ah (high energy), Lithium Iron Phosphate 14 Ah (high power) and Lithium Titanate Oxide 5 Ah (high power), providing a range of different cell characteristics and capacities. An updated workflow for the development of the ECM model is presented which includes extended versions of previous characterization and parameterization procedures used to populate a 2nd Order Thévenin ECM topology. The model is able to use two types of charge estimations, the extended coulomb counting and the extended Kalman filter techniques. The accuracy of the simulation in all three chemistries is increased through this improved characterization and optimization procedures. The “Initial State of Charge value”, “Capacity Value”, “Internal Resistance value” and the “Open Circuit Voltage” are included inside the complete model and have shown to affect greatly the accuracy of the simulations, specifically when the extended coulomb counting technique is implemented. The State of Health (SoH) level the validation profile was characterize in combination with the total time the simulation is performed have shown to affect also the accuracy of the simulation. The complete developed model is able to be combined with thermal and ageing models of lithium-ion cells. Combining this with the extended database of validated simulations for the different chemistries and temperatures, provides a suitable model to be extended to pack-level models of battery packs.

Fast computation of the electrolyte-concentration transfer function of a lithium-ion cell model

One approach to creating physics-based reduced-order models (ROMs) of battery-cell dynamics requires first generating linearized Laplace-domain transfer functions of all cell internal electrochemical variables of interest. Then, the resulting infinite-dimensional transfer functions can be reduced by various means in order to find an approximate low-dimensional model. These methods include Padé approximation or the Discrete-Time Realization algorithm.In a previous article, Lee and colleagues developed a transfer function of the electrolyte concentration for a porous-electrode pseudo-two-dimensional lithium-ion cell model. Their approach used separation of variables and Sturm–Liouville theory to compute an infinite-series solution to the transfer function, which they then truncated to a finite number of terms for reasons of practicality. Here, we instead use a variation-of-parameters approach to arrive at a different representation of the identical solution that does not require a series expansion. The primary benefits of the new approach are speed of computation of the transfer function and the removal of the requirement to approximate the transfer function by truncating the number of terms evaluated. Results show that the speedup of the new method can be more than 3800.

Finite element model approach of a cylindrical lithium ion battery cell with a focus on minimization of the computational effort and short circuit prediction

In this research, a parameterized beam-element-based mechanical modeling approach for cylindrical lithium ion batteries is developed. With the goal to use the cell model in entire vehicle crash simulations, focus of development is on minimizing the computational effort whilst simultaneously obtaining accurate mechanical behavior. The cylindrical cell shape is approximated by radial beams connected to each other in circumferential and longitudinal directions. The discrete beam formulation is used to define an anisotropic material behavior. An 18650 lithium ion cell model constructed in LS-Dyna is used to show the high degree of parameterization of the approach. A criterion which considers the positive pole deformation and the radial deformation of the cell is developed for short circuit prediction during simulation. An abuse testing program, consisting of radial crush, axial crush, and penetration is performed to evaluate the mechanical properties and internal short circuit behavior of a commercially available 18650 lithium cell. Additional 3-point-bending tests are performed to verify the approach objectively. By reducing the number of strength-related elements to 1600, a fast and accurate cell model can be created. Compared to typical cell models in technical literature, simulation time of a single cell load case can be reduced by approx. 90%.

Controls-oriented models of lithium-ion cells having blend electrodes. Part 1: Equivalent circuits

Battery-management systems rely on mathematical sets of equations known as models when implementing battery controls procedures. Models are used in state-of-charge, state-of-health, available-energy, and available-power estimation tasks. These models should be high fidelity for good estimates but also computationally lightweight for inexpensive implementation.This paper and its Part-2 companion concern themselves with simple but accurate models of lithium-ion cells having composite electrodes, which are composed of a blend of multiple active materials. In this paper, we develop two forms of equivalent-circuit model (ECM): the series ECM and the parallel ECM—and show how to find values for the model parameters using current–voltage input–output data. We compare simulations of the ECMs to truth data from simulations of a full-order model and show that an ECM designed with knowledge of the material blend can outperform a standard ECM of similar complexity. In the companion paper, we show that it is further possible to create physics-based reduced-order models that have greater predictive power.

Controls-oriented models of lithium-ion cells having blend electrodes. Part 2: Physics-based reduced-order models

Physics-based battery models can predict not only voltage behaviors of a cell but also internal electrochemical variables such as lithium concentrations and electrical potentials. Knowledge of these variables will be critical in future battery management systems to be able to devise controls that extract the maximum performance from a cell while also slowing down its degradation, since available performance and degradation are both direct functions of the values of these internal electrochemical variables.This paper and its Part-1 companion concern themselves with simple but accurate models of lithium-ion cells having electrodes that are composed of a blend of multiple active materials. In this paper, we show how to create a physics-based reduced-order model (ROM). This ROM not only gives better voltage predictions than the equivalent-circuit models proposed in the Part-1 paper, but is also able to predict all cell internal electrochemical variables. Additionally, its computational complexity is similar to that of the circuit model.

Mars Express Lithium Ion Batteries Performance Analysis

Now more than 12 years in orbit, Mars Express battery telemetry during some of the deepest discharge cycles has been analysed with the help of the ESTEC lithium ion cell model. The best-fitting model parameter sets were then used to predict the energy that is expected to be available before the battery voltage drops below the minimum value that can support the power bus. This allows mission planners to determine what future power profiles could be supported without risk of entering safe mode. It also gives some more insights into the ageing properties of these batteries.

Two-Dimensional Thermal Modeling of Lithium-Ion Battery Cell Based on Electrothermal Impedance Spectroscopy

Thermal modeling of lithium-ion batteries is gaining its importance together with increasing power density and compact design of the modern battery systems in order to assure battery safety and long lifetime. Thermal models of lithium-ion batteries are usually either expensive to develop and accurate or equivalent thermal circuit based with moderate accuracy and without spatial temperature distribution. This work presents initial results that can be used as a fundament for the cost-efficient development of the two-dimensional thermal model of lithium-ion battery based on multipoint electrothermal impedance spectroscopy.

A novel phenomenological multi-physics model of Li-ion battery cells

Abstract A novel phenomenological multi-physics model of Lithium-ion battery cells is developed for control and state estimation purposes. The model can capture electrical, thermal, and mechanical behaviors of battery cells under constrained conditions, e.g., battery pack conditions. Specifically, the proposed model predicts the core and surface temperatures and reaction force induced from the volume change of battery cells because of electrochemically- and thermally-induced swelling. Moreover, the model incorporates the influences of changes in preload and ambient temperature on the force considering severe environmental conditions electrified vehicles face. Intensive experimental validation demonstrates that the proposed multi-physics model accurately predicts the surface temperature and reaction force for a wide operational range of preload and ambient temperature. This high fidelity model can be useful for more accurate and robust state of charge estimation considering the complex dynamic behaviors of the battery cell. Furthermore, the inherent simplicity of the mechanical measurements offers distinct advantages to improve the existing power and thermal management strategies for battery management.

The Clay-like Mechanics Model of Cylindrical Lithium-Ion Battery Cells under Radial Compression

A simple load case was chosen to reveal the essential mechanics properties of cylindrical lithium-ion battery and it was found that its mechanics characteristic is clay-like, according to the plastic flow rule. Then, a linear equation was proposed to describe the nonlinear constitutive behavior of cylindrical lithium-ion battery, which will lay a foundation for constructing the system of battery mechanics, according to the mechanics characteristic of clay.

Bayesian calibration for electrochemical thermal model of lithium-ion cells

Pseudo-two dimensional electrochemical thermal (P2D-ECT) model contains many parameters that are difficult to evaluate experimentally. Estimation of these model parameters is challenging due to computational cost and the transient model. Due to lack of complete physical understanding, this issue gets aggravated at extreme conditions like low temperature (LT) operations. This paper presents a Bayesian calibration framework for estimation of the P2D-ECT model parameters. The framework uses a matrix variate Gaussian process representation to obtain a computationally tractable formulation for calibration of the transient model. Performance of the framework is investigated for calibration of the P2D-ECT model across a range of temperatures (333 K263 K) and operating protocols. In the absence of complete physical understanding, the framework also quantifies structural uncertainty in the calibrated model. This information is used by the framework to test validity of the new physical phenomena before incorporation in the model. This capability is demonstrated by introducing temperature dependence on Bruggeman's coefficient and lithium plating formation at LT. With the incorporation of new physics, the calibrated P2D-ECT model accurately predicts the cell voltage with high confidence. The accurate predictions are used to obtain new insights into the low temperature lithium ion cell behavior.

(Invited) The Use of Modeling to Reveal Root-Cause and Quantify Degradation Effects in Electrochemical Systems

Electrochemical systems are characterized by coupled, non-linear behavior of several phenomena. Typically, thermodynamics, kinetics, and mass-transfer all come in to play in describing the current voltage response of a system. This strong coupling can make interpretation of experimental results confounding and cause our intuition to fail us. Through, mathematical modeling, the nature of the response is more easily revealed. This concept is explored through two real-world applications of electrochemical systems: start-stop phenomena in fuel cells and power fade in lithium-ion batteries. Corrosion of carbon support during start-up and shut-down of proton-exchange-membrane fuel cells is well-known and widely reported in the literature. Today, this is an accepted degradation mechanism. However, the journey from severe performance loss observed in a fuel-cell vehicle to our present understanding was difficult. In fact, measurements of cell potential and current did not help elucidate the mechanism at all. It was only through mathematical modeling that the corrosion process was clarified. No new physics was needed, just the careful assembly of existing knowledge of kinetics and transport for a start-up transient. Capacity fade in lithium-ion batteries is also a well-known issue. Generally, the formation and slow growth of the solid electrolyte interphase (SEI) results in irreversible consumption of lithium. This loss of cyclable lithium translates into a reduced capacity of the battery with age. In addition to capacity fade, power fade is critical for many applications. A prime example is the battery for a charge-sustaining hybrid-electric vehicle. Here, the energy storage system is used for recovering energy and power assist, not sustained propulsion of the vehicle. Therefore, power capability is at least if not more important than capacity. The power capability is characterized by “cell resistance.” As the SEI thickness grows, the ohmic resistance of the cell increases. However, the magnitude of the increase cannot explain the power fade. Typically, for a pulse of current of ten or so seconds is used in practice to measure “cell resistance.” For transients of this length, this quantity is not simply the ohmic resistance of the cell--concentration polarizations are significant. This behavior is explored with well-established mathematical models of lithium-ion cells. Again, a mathematical model that uses existing physics is able to shed light on the nature of the power fade.

A Semi-Empirical Capacity Fade Model for Lithium Ion Cells with Nickel Based Composite Cathode

High energy density and low cost of nickel based composite cathode has drawn significant attention for vehicular application of Li-ion battery. Experimental observations confirm that the capacity fade of such cells are governed by the surface degradation of the cathode particles. Although, there are many experimental studies on this phenomenon, no numerical model exists. In the present investigation a semi-empirical and semi-electrochemical model is proposed based on the experimental results. The cathode degradation based hypothesis is found to be valid on experimental data obtained at varied operating temperature and discharge rates. A physics based model has been derived from the hypothesis. As the cathode degradation reaction is kinetically driven, the capacity-fade model has been decoupled from the standard electrochemistry based battery model, making it computationally economical. Due to this ease of computation, the present approach can be used to estimate the capacity loss due to cathode degradation without detailed electrochemical models and cyclic simulations. The model has shown excellent predictive capability when compared with experimental data for a wide range of operating conditions. Therefore, the model is ideal for an onboard battery management system as well as for a prognostic tool for battery life prediction along with other algorithms.

Rapid Analysis of Charging Profiles of Lithium Ion Batteries Using a Hybrid Simplified Electrochemical Model

Persistent energy demands of portable electronic devices necessitate the development of efficient charging protocols for the lithium ion cells powering these applications. In addition to a minimization in charging time and cell degradation, an optimal profile needs to ensure the maximization of lithium intercalation in the electrodes. Thus an electrochemical understanding of the system is highly beneficial in the design of efficient charging profiles. In this work, in order to identify and assess charging profiles, the essential features of an electrochemical model is combined with a phenomenological nonlinear resistor description to develop a simplified hybrid electrochemical model for lithium ion cells. This structure of the model allows for the simultaneous fast evaluation of charging profiles at the same time capturing the essential physical processes. Common charging protocols rely on a constant voltage charging segment, which is implemented here by the use of a new implicit analytical expression obtained for the charging current. The model outputs in various conditions are compared with experiments conducted on a commercial battery. Subsequently, alternate charging candidates are assessed using the model. To highlight the capability of the model, cyclic charge-discharge studies are conducted to quickly assess the degradation effects of the various charging profiles.

Electro-Thermal Modeling of Large Format Lithium-Ion Pouch Cells: A Cell Temperature Dependent Linear Polarization Expression

In the work presented here, a well-known semi-empirical electro-thermal model of large format lithium-ion pouch cells is extended by accounting for a cell temperature dependency of electrode polarization gained from full cell measurement. For model parametrization, the cell was discharged at varying discharge rates and ambient temperatures within a climate chamber. By relating the measured cell potential to its current temperature, a cell temperature dependency of cell polarization is established. Evaluating the advantages of this approach, the extended model is compared to the initial model regarding the quality of predicting the electrical and thermal cell behavior. For further means of model validation, the cell was investigated at cooling conditions varying from the parametrization measurements via infrared thermography. It can be shown that a temperature dependency of electrode polarization shows superior quality especially when predicting the overall electrical and thermal cell performance at ambient conditions varying from the parametrization scenario. Controlling the thermal boundary conditions further allows to evaluate the impact of local heat generation on the temperature distribution. For a laminar, directed airflow of 1 m/s along the cell, the influence of local heat generation is minor in comparison to the thermal boundary conditions prevailing at the cell’s surface and tabs.

A reduced order electrochemical thermal model for lithium ion cells

A reduced order model (ROM) is proposed for accurate prediction of electrochemical and thermal response of lithium ion cells. The order reduction is carried on the coupled partial differential equations (PDE) of the electrochemical thermal model by consistent volume averaging of local heat generation and spatial temperature variation. The model is validated with experimental data for temperatures ranging from 253 K–333 K. It is seen that modification of ROM to account for low electronic conductivity results in accurate voltage estimation of cells with lithium nickel cobalt aluminium oxide (LNCO) cathodes. A detailed parametric sensitivity to operating conditions is provided. The utility of ROM for on-board state estimation is demonstrated by applying to realistic drive cycle protocols such as the Hybrid Pulse Power Characterization (HPPC) and the Urban Dynamometer Driving Schedule (UDDS) data. The electrochemical structure of ROM enables identification of controlling processes, and analysis of HPPC results reveal that Ohmic drop of cathode is controlling at high rates and the electrolyte potential during rest phase. Based on accurate voltage prediction, computational speed and physical insights, it can be concluded that the proposed ROM is an adequate state estimation and a cell design tool.

Non-isothermal electrochemical model for lithium-ion cells with composite cathodes

Transition metal oxide cathodes for Li-ion batteries offer high energy density and high voltage. Composites of these materials have shown excellent life expectancy and improved thermal performance. In the present work, a comprehensive non-isothermal electrochemical model for a Lithium ion cell with a composite cathode is developed. The present work builds on lithium concentration-dependent diffusivity and thermal gradient of cathode potential, obtained from experiments. The model validation is performed for a wide range of temperature and discharge rates. Excellent agreement is found for high and room temperature with moderate success at low temperatures, which can be attributed to the low fidelity of material properties at low temperature. Although the cell operation is limited by electronic conductivity of NCA at room temperature, at low temperatures a shift in controlling process is seen, and operation is limited by electrolyte transport. At room temperature, the lithium transport in Cathode appears to be the main source of heat generation with entropic heat as the primary contributor at low discharge rates and ohmic heat at high discharge rates respectively. Improvement in electronic conductivity of the cathode is expected to improve the performance of these composite cathodes and pave way for its wider commercialization.

A Parametric Open Circuit Voltage Model for Lithium Ion Batteries

We present an open circuit voltage (OCV) model for lithium ion (Li-ion) cells, which can be parameterized by measurements of the OCV of positive and negative electrode half-cells and a full cell. No prior knowledge of physical parameters related to particular cell chemistries is required. The OCV of the full cell is calculated from two electrode sub-models, which are comprised of additive terms that represent the phase transitions of the active electrode materials. The model structure is flexible and can be applied to any Li-ion cell chemistry. The model can account for temperature dependence and voltage hysteresis of the OCV. Fitting the model to OCV data recorded from a Li-ion cell at 0°C, 10°C, 20°C, 30°C and 40°C yielded high accuracies with errors (RMS) of less than 5 mV. The model can be used to maintain the accuracy of dynamic Li-ion cell models in battery management systems by accounting for the effects of capacity fade on the OCV. Moreover, the model provides a means to separate the cell's OCV into its constituent electrode potentials, which allows the electrodes’ capacities to be tracked separately over time, providing an insight into prevalent degradation mechanisms acting on the individual electrodes.

Capacity and power fade cycle-life model for plug-in hybrid electric vehicle lithium-ion battery cells containing blended spinel and layered-oxide positive electrodes

This paper proposes and validates a semi-empirical cycle-life model for lithium-ion pouch cells containing blended spinel and layered-oxide positive electrodes. For the model development and validation experimental data obtained during an aging campaign is used. During the campaign the influence of charge sustaining/depleting operation, minimum state of charge (SOC), charging rate and temperature on the aging process is studied. The aging profiles, which are prescribed in power mode, are selected to be representative of realistic plug-in hybrid electric vehicle (PHEV) operation. The proposed model describes capacity fade and resistance increase as function of the influencing stress factors and battery charge throughput. Due to its simplicity but still good accuracy, the applications of the proposed aging model include the design of algorithms for battery state-of-health (SOH) monitoring and prognosis, PHEV optimal energy management including battery aging, and the study of aging propagation among battery cells in advanced energy storage systems.

Nonlinear Filtering Techniques Comparison for Battery State Estimation

The performance of estimation algorithms is vital for the correct functioning of batteries in electric vehicles, as poor estimates will inevitably jeopardize the operations that rely on un-measurable quantities, such as State of Charge and State of Health. This paper compares the performance of three nonlinear estimation algorithms: the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter, where a lithium-ion cell model is considered. The effectiveness of these algorithms is measured by their ability to produce accurate estimates against their computational complexity in terms of number of operations and execution time required. The trade-offs between estimators' performance and their computational complexity are analyzed.