P2D Model Research Articles

A General Three-Dimensional Electrochemical-Thermal Modeling Framework to Study Large-Format Batteries

Lithium-ion batteries’ performance, degradation, and safety are highly sensitive to their operating temperature [1-3]. Depending upon the form-factor, construction, and thermal boundary conditions, large temperature variations may be present within a battery in more than one direction. Physics-based battery models, such as single-particle model (SPM), enhanced single-particle model (ESPM), tank-in-series model, and the widely used pseudo-two-dimensional (p2D) model, ignore the effect of temperature variations in one or more directions [4]. Specifically, p2D model can resolve temperature variation within anode, cathode, and separator of a single stack but this is often not useful as the temperature variation within a single stack will be negligible due to the small length scale. Also, a commercial-scale Li-ion battery is a multi-stack system with possibly significant temperature variation across the stacks as compared to within a single stack. The recently developed thermal tank-in-series battery model accounts for temperature variation across a multi-stack battery system but does not account for temperature variation in the direction parallel to the current collector [5]. In the case of large-format batteries, significant temperature variations are also expected along the directions corresponding to the longer dimensions. This would typically involve temperature variations in the directions parallel to the current collector. Multi-scale multi-domain (MSMD) models have been developed in the past to extend the single-stack level physics-based models to account for temperature nonuniformity in these directions [6-8]. However, temperature variation in the direction corresponding to the shortest dimension may also be appreciable due to the anisotropic/orthotropic nature of heat transfer in the battery system at the macroscale [9,10]. This is because the heat transfer in this direction may be severely impeded by the multi-stack construct leading to poor thermal conductivity in that direction. This in turn may lead to a large temperature gradient even along the direction corresponding to the shortest dimension of the large-format battery system. This suggests the need for careful formulation of MSMD battery models considering the construction, design parameters, and external thermal conditions of a particular battery system. In the present work, we propose a general three-dimensional modeling framework that accounts for the effect of the three-dimensional temperature field on the local variations in thermodynamics, transport processes, and reaction kinetics in the battery system. This type of battery modeling framework can be used to study nonuniform temperature distribution driven spatially uneven degradation, particularly in large-format batteries. Additionally, this modeling framework can help design physics-aware battery-specific thermal management systems to improve performance and reduce degradation. This will be a drastic departure from the present approach of designing battery thermal management system which treats the battery in a rather simplistic manner.

Study on Lithium-Ion Battery Degradation Caused by Side Reactions in Fast-Charging Process

With the development of electric vehicles, fast-charging is greatly demanded for commercialisation on lithium-ion batteries. The rapid charging process could lead to serious side reactions on the graphite anodes, such as lithium plating and solid electrolyte interface (SEI) film growth, which severely affect the battery performances. However, there is a lack of quantitative research on their contribution ratio to battery performance and the occurrence thresholds. In this work, a P2D model of a lithium-ion battery with the correction of SEI film growth and lithium plating was built. A cyclic charge/discharge experiment was also designed to analyze the changes of SEI film and lithium plating under high charge-rate conditions. It was found that under such conditions, the battery capacity attenuation in the early stage was mainly caused by lithium plating. In the middle and late stages, as the lithium plating tended to be stable, the capacity attenuation was largely caused by the growth of the SEI film. The study provides theoretical support for the improvement of the charge/discharge strategy of lithium-ion batteries.

A Tanks-in-Series Approach to Estimate Parameters for Lithium-Ion Battery Models

Advanced Battery Management Systems (BMS) play a vital role in monitoring, predicting, and controlling the performance of lithium-ion batteries. BMS employing sophisticated electrochemical models can help increase battery cycle life and minimize charging time. However, in order to realize the full potential of electrochemical model-based BMS, it is critical to ensure accurate predictions and proper model parameterization. The accuracy of the predictions of an electrochemical model is dependent on the accuracy of its parameters, the values of which might change with battery cycling and aging. Parameter estimation for an electrochemical model is generally challenging due to the nonlinear nature and computational complexity of the model equations. To this end, this work utilizes the recently proposed Tanks-in-Series model for Li-ion batteries (J.Electrochem. Soc., 167, 013534 (2020)) to perform parameter estimation. The Tanks-in-Series approach allows for substantially faster parameter estimation compared to the original pseudo two-dimensional (p2D) model. The objective of this work is thus to demonstrate the gain in computational efficiency from the Tanks-in-Series approach. A sensitivity analysis of model parameters is also performed to benchmark the fidelity of the Tanks-in-Series model.

Thermal management of 18650 Li-ion battery using novel fins–PCM–EG composite heat sinks

The present study introduces a novel fin–Phase Change Material (PCM)–Expanded Graphite (EG) composite for better thermal management of a Panasonic NCR18650BD battery at discharge rates higher than its maximum discharge limit 2C. Fins and EG are augmented with PCM to enhance its effective thermal conductivity. Initially, the electrical and thermal behaviors of the battery are simulated for 0.5, 1, and 2C discharge rates using the Newman P2D model, and these are validated against in-house experiments. Following this, the heat generation profiles are estimated from the numerical model to mimic the battery with a heater in the experiments conducted to propose an effective thermal management system for 2, 3, and 4C discharge rates. Three heat sinks, one sans fins, and the other two with 130 and 260 fins, respectively, are considered to perform experiments. Phase Change Material (PCM) named Eicosane (Ei) with an addition of 0, 10, 20, 25, and 30% weight fractions of EG is filled in the heat sinks to study the effect of composite PCM on the thermal regulation of the battery. The heat sink having 260 fins filled with 70% Ei - 30% EG composite outperforms the other heat sinks considered in this study by recording lower temperatures to the extent of 17.5, 20.5, and 22.7 °C than a plain heat sink filled with 100% Eicosane for discharge rates 2, 3, and 4C, respectively. Furthermore, with the addition of 30% EG by volume, the maximum thermal performance of heat sink having 130 fins surpasses the heat sink having 260 fins filled with pure Eicosane by recording 1.3, 0.5, and 1.5 °C lower temperatures for discharge rates 2, 3, and 4C, respectively. In view of this, a possible engineering solution is to employ a simple heat sink, having fewer fins filled with PCM–EG composite instead of intricate heat sinks, having more fins filled only with the baseline PCM, to overcome the design difficulties and manufacturing costs.

Simplification of full homogenized macro-scale model for lithium-ion batteries

A simplified model based on the novel full homogenized macro-scale model (FHM) is proposed to reduce the computational time of the FHM model with trivial loss of fidelity. The simplified FHM model is compared with a simplified model based on the pseudo-two-dimensional (P2D) model. The FHM model is based on the homogenization theory, while the volume averaging technique is the basis of the P2D model. Diffusion Partial differential equations (PDEs) are approximated by ordinary differential equations with time-varying coefficients. The intercalation current and conduction equation are also approximated to develop variants of the simplified model. The diffusion and reaction rate parameters of the FHM model are more accurate at high temperatures than the parameters based on the empirical Bruggeman method, as the FHM model parameters are based on the numerical model of the electrode structure. The simulations results verify that, compared with a similar simplified model based on the P2D model, the proposed simplified FHM model is more accurate at 318 K and higher temperature. The output voltage predicted by the proposed simplified model and the simplified P2D model has a root mean square (RMS) tracking error of 0.6% and 2%, respectively, at 1 C input current and 318 K temperature. The computational time of the proposed simplified model is reduced by 35% compared with that of the FHM model, highlighting its superior performance. Discretization of the model is accomplished using orthogonal collocation.

Analysis of the lithium-ion battery capacity degradation behavior with a comprehensive mathematical model

The influence of transition metal deposition on the capacity of lithium-ion batteries (LIBs) can not be ignored. The current model lacks a comprehensive analysis of the coupling phenomenon. Based on the classic P2D model, we propose a comprehensive capacity degradation model of LIBs, with a complete description of the side effects of transition metal dissolution in the positive electrode, solid electrolyte interphase (SEI) formation, and metal deposition in the negative electrode. Simulations are implemented and compared for the evolution of the battery capacity as cycling progressed in different cases of only SEI layer growth, SEI growth couples with Li plating, SEI growth couples with Mn dissolution and deposition, and all the three factors fully couples. The capacity degradation behavior is revealed from the perspective of lithium-ion inventory, diffusion coefficient, and porosity. The results show that the plating of Li leads to a significant decrease of the lithium-ion concentration, which is the prime for the attenuation of capacity. The growth of SEI alone has little effect on the capacity, which maintains 95.9% even after 2500 cycles. Although the dissolved content of Mn is just ppm scale, it can accelerate the growth of SEI layer and thus obviously affect the battery capacity. • Presenting a comprehensive lithium-ion battery model. • A lithium-ion battery model to predict capacity degradation. • Revealing the coupling relationship of side reactions. • Clarifying the influence level of each side reaction on capacity degradation. • The model fully reflects the behavior of Mn-ions.

Numerical analysis of a finite element formulation of the P2D model for Lithium-ion cells

The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics of lithium-ion batteries. In this paper, we present the numerical analysis of a finite element-implicit Euler scheme for such a model. We obtain error estimates for both the spatially semidiscrete and the fully discrete systems of equations, and establish the existence and uniqueness of the fully discrete solution.

Comparison and Combination of Pseudo Two-Dimensional and Machine Learning Models for Prediction of Electrochemical Properties of Thick Sintered Lithium-Ion Battery Electrodes

Investigations of lithium-ion battery materials and processing continues to grow as the performance demands for energy storage applications increases. Modeling tools can facilitate more time and cost efficient investigation of new battery materials and processing. Ideally, these tools will predict with reasonable accuracy relevant battery performance outcomes as a function of the parameters being modified to reduce the experimental system space. However, there are limits to the information and data sizes available to train the models in the case of machine learning (ML) algorithms, and for physics-based models often obtaining every necessary physical property, including the variation in those properties as a function of electrochemical sample space is also a challenge. For this study, a physics-based pseudo two-dimensional (P2D) model was used to predict the cycling behavior of thick sintered lithium-ion battery electrodes. In addition, multiple ML algorithms were applied to data collected on sintered electrodes of varying compositions. This work will describe comparisons between using a ML approach, a P2D model, and a hybrid where the P2D model provides an additional input to the ML algorithm.

Overpotential analysis of graphite-based Li-ion batteries seen from a porous electrode modeling perspective

The overpotential of Li-ion batteries is one of the most relevant characteristics influencing the power and energy densities of these battery systems. However, the intrinsic complexity and multi-influencing factors make it challenging to analyze the overpotential precisely. To decompose the total overpotential of a battery into various individual components, a pseudo-two-dimensional (P2D) model has been adopted and used for electrochemical simulations of a graphite-based porous electrode/Li battery. Analytical expressions for the total overpotential have been mathematically derived and split up into four terms, associated with the electrolyte concentration overpotential, the Li concentration overpotential in the solid, the kinetic overpotential, and the ohmic overpotential. All these four terms have been separately analyzed and are found to be strongly dependent on the physical/chemical battery parameters and the reaction-rate distribution inside the porous electrode. The reaction-rate distribution of the porous electrode is generally non-uniform and shows dynamic changes during (dis)charging, resulting in fluctuations in the four overpotential components. In addition, the disappearance of the phase-change information in the voltage curve of the graphite-based porous electrode/Li battery under moderate and high C-rates is ascribed to the Li concentration overpotential among solid particles, resulting from the non-uniform reaction-rate distribution. • Analytical overpotential expressions are derived from P2D model. • Four overpotential components contribute to the total battery overpotential. • Four overpotential components are coupled together by the reaction rate distribution. • Fluctuations in overpotential components are related to the reaction rate distribution.

Transport In and Optimization of Aligned-Channel Li-Ion Electrode Architectures

Advanced electrode architectures utilizing aligned channels show promise in improving rate performance. However, the relationship between aligned channel structure and electrode-scale ion transport rate must be understood to enable optimization of electrode designs. Using a physics-based P2D model for experimental analysis, the impact of aligned channel electrode structures on cell rate capability is quantified. Results are used for optimization of aligned-channel volume fraction and electrode mass loading. Anticipated improvements in volumetric energy density over optimal for conventional, slurry-cast electrodes are shown to be significant at high rates and with electrodes characterized by high tortuosity.

Quantifying Uncertainty in Tortuosity Estimates for Porous Electrodes

Measuring tortuosity in porous electrodes is important for understanding rate capability and optimizing design. Here, we describe an approach to determine electrode tortuosities and quantify the associated uncertainties by fitting a P2D model to discharge profiles from a standard rate capability test. A dimensionless current is identified as a design-of-experiment parameter that can be used to identify experiments that return confident estimates of tortuosity, even when other model parameters are not known with certainty. This approach is applied to analysis of (LVO) electrodes and (NMC) electrodes. The details of the assumptions made in these measurements and their impact on the reported uncertainties are discussed. We also perform an uncertainty analysis on the standard method for quantifying tortuosity in the literature: electrochemical impedance spectroscopy collected under blocking electrolyte conditions. We find that confident estimates can be obtained using this approach even when uncertainties in equivalent circuit model parameters are considered.

Determination of state-of-charge dependent diffusion coefficients and kinetic rate constants of phase changing electrode materials using physics-based models

The simplified gravimetric intermittent titration technique (GITT) model, which was first proposed by Weppner and Huggins in 1977, remains a popular method to determine the solid-state diffusion coefficient ( D 1 ) and the electrochemical kinetic rate constant ( k ). This is despite the model having been developed on the premise of a single-slab electrode and other gross simplification which are not applicable to modern-day porous battery electrodes. Recently however, more realistic and conceptually descriptive models have emerged, which make use of the increased availability of computational power. Chief among them is the P2D model developed by Newman et al., which has been validated for various porous battery electrodes. Herein, a P2D GITT model is presented and coupled with grid search optimization to determine state-of-charge (SOC) dependent D 1 and k parameters for a sodium-ion battery (SIB) cathode. Using this approach, experimental GITT steps could be well fitted and thus validated at different SOC points. This work demonstrates the first usage of the P2D GITT model coupled with optimization as an analytical method to derive and validate physically meaningful parameters. The accurate knowledge of D 1 and k as a function of the SOC gives further insight into the SIB intercalation dynamics and rate capability. • A P2D model and GITT experiments on a Na// sodium-ion battery half-cell are presented. • SOC dependent diffusion coefficient and kinetic rate constant are derived from the P2D model and grid search optimization. • The model accurately matches the experimental voltage profiles in the solid-solution and phase transition regions. • This approach is a departure from usual analytical models and provides physically meaningful electrochemical parameters.

A Control-Oriented Single Particle Model with Electrolyte Dynamics and Stress-Diffusion Coupling

Full electrochemical models are well-established as the standards for accurately predicting battery behavior. These are especially useful for cell design since performance can be evaluated based on various model parameters. Conventional models can be coupled with additional physics such as diffusion-induced stress, crack propagation, and battery degradation mechanisms to test different physical phenomena. However, these models are too computationally intensive to implement in battery management systems (BMSs), which utilize control and estimation algorithms to monitor performance and ensure safety. Single particle models (SPMs), which are computationally efficient approximations of pseudo-two-dimensional (P2D) models, are often used instead. However, most SPMs are only valid for low C-rates. In this paper, a new ODE-based SPM is proposed that captures high C-rate effects by including electrolyte physics and stress-diffusion coupling. Models describing these physics are validated by comparing simulation results to the P2D model at several C-rates. A single lumped parameter is used to quantify the intensity of the stress-diffusion coupling in an electrode. Simulation results are presented to show how variation of this parameter affects charge-discharge cycle times at different C-rates. Next, the improved SPM is linearized and presented as both state space and transfer function models. The frequency responses of the linearized SPM and P2D model are compared with and without stress-diffusion coupling. Further, the effects of varying the stress-diffusion coupling intensity on the frequency response are discussed. The proposed linearized model is more computationally efficient than full electrochemical and P2D models, and includes key physics that are missing in most low-order battery models. As a result, the proposed model is well-suited for a wide variety of BMS applications and offers improvements at high C-rates that are necessary for fast charging applications.

Estimation of Grouped Parameters Using Tanks-in-Series Lithium-Ion Battery Model

Parameter estimation is critical for efficient Battery Management System (BMS) performance. The accuracy and predictability of a model depends on the precision of its parameters. Moreover, model parameters tend to change with battery aging. Efficient BMS performance requires accurate tracking and updating of relevant parameters as the battery ages. Estimating parameters for electrochemical models is challenging due to the complexity of the governing equations, and the possibility of degeneracy, with multiple sets of parameter values that give the same accuracy for fitting charge/discharge data. Parameter estimation of various lithium-ion battery systems has been attempted with different model types, including equivalent circuit model2, single particle model3 and pseudo 2D (P2D) model.4,5 Estimation approaches reported in literature, such as, GA6, heuristic algorithms7, etc., are difficult to implement in real-time due to computational complexity. In the past, we proposed and implemented reformulated p2D models for real-time parameter estimation.8,9 While the reformulated models are computationally inexpensive, the large set of parameters and resulting likelihood of degeneracy introduce substantial complexity. Recently, we proposed lithium-ion Tanks-in-Series battery model10. This model is generated by systematic volume-averaging of the p2D model that enables efficient and real-time simulation with reduced set of parameters.In this presentation, we propose to estimate non-dimensional grouped parameters using non-dimensional Tanks-in-Series battery model. The grouping of parameters further reduces the number of parameters that needs to be estimated. This also reduces the computational effort required to perform optimization. The non-dimensional model captures resistances offered due to transport, reaction kinetics, and ohmic drop in electrolyte based on the non-dimensional grouped parameters that absorb constitutive expressions and parameters, such as electrolyte diffusivity, ionic conductivity, reaction rate constants and solid phase diffusivity. The estimation is performed on experimental charge/discharge data obtained from cylindrical cells having NCA and NMC cathode chemistries. The accuracy of the estimated parameters is validated using experimental cycling data obtained at different c-rates by calculating the error in voltage-time curves between the model prediction using estimated parameters and the experimental data. Acknowledgements The authors acknowledge funding from the U.S. Department of Energy Office of Electricity Energy Storage Program through Sandia National Laboratories, under the guidance of Dr. Imre Gyuk, and the Texas Materials Institute at The University of Texas at Austin. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy National Nuclear Security Administration under contract DE-NA-0003525. SAND2020-14131 A References V. Ramadesigan, P. W. C. Northrop, S. De, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 159, R31–R45 (2012).Y. Hu, S. Yurkovich, Y. Guezennec, and B. J. Yurkovich, Control Eng. Pract., 17, 1190–1201 (2009).A. P. Schmidt, M. Bitzer, Á. W. Imre, and L. Guzzella, IFAC Proc. Vol., 43, 198–203 (2010).J. C. Forman, S. J. Moura, J. L. Stein, and H. K. Fathy, in 5th Annual Dynamic Systems and Control Conference,, p. 1–8 (2012).S. Santhanagopalan, Q. Guo, and R. E. White, J. Electrochem. Soc., 154, 198–206 (2007).A. Jokar, B. Rajabloo, M. Désilets, and M. Lacroix, J. Electrochem. Soc., 163, A2876–A2886 (2016).J. Li, L. Zou, F. Tian, X. Dong, Z. Zou, and H. Yang, J. Electrochem. Soc., 163, A1646–A1652 (2016).V. Boovaragavan, S. Harinipriya, and V. R. Subramanian, J. Power Sources, 183, 361–365 (2008).V. Ramadesigan, K. Chen, N. A. Burns, V. Boovaragavan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 158, A1048–A1054 (2011).A. Subramaniam, S. Kolluri, C. D. Parke, M. Pathak, S. Santhanagopalan, and V. R. Subramanian, J. Electrochem. Soc., 167, 013534-013534–18 (2020).

Electrochemical Model-Based Investigation of Thick LiFePO4 Electrode Design Parameters

The electrification of the powertrain requires enhanced performance of lithium-ion batteries, mainly in terms of energy and power density. They can be improved by optimising the positive electrode, i.e., by changing their size, composition or morphology. Thick electrodes increase the gravimetric energy density but generally have an inefficient performance. This work presents a 2D modelling approach for better understanding the design parameters of a thick LiFePO4 electrode based on the P2D model and discusses it with common literature values. With a superior macrostructure providing a vertical transport channel for lithium ions, a simple approach could be developed to find the best electrode structure in terms of macro- and microstructure for currents up to 4C. The thicker the electrode, the more important are the direct and valid transport paths within the entire porous electrode structure. On a smaller scale, particle size, binder content, porosity and tortuosity were identified as very impactful parameters, and they can all be attributed to the microstructure. Both in modelling and electrode optimisation of lithium-ion batteries, knowledge of the real microstructure is essential as the cross-validation of a cellular and lamellar freeze-casted electrode has shown. A procedure was presented that uses the parametric study when few model parameters are known.

Physico-chemical parameter measurement and model response evaluation for a pseudo-two-dimensional model of a commercial lithium-ion battery

To effectively evaluate battery performance by means of electrochemical modelling, a consistent set of parameters is essential. The aim of this work is to provide a complete physico-chemical methodology to measure all the necessary parameters for a pseudo-two-dimensional (P2D) electrochemical model. Component composition, thermodynamic, kinetic and transport properties, parameters related to the porous structures, internal battery configuration and full-cell electrode balancing are presented for a commercial lithium-ion battery. Then, the measured parameters are entered into the P2D model, and battery responses are evaluated against full-cell experimental curves (galvanostatic charge-discharge at different current rates, EIS responses and pulses) to correlate numerical-experimental results.

Reduced-order electrochemical model for lithium-ion battery with domain decomposition and polynomial approximation methods

The pseudo-two-dimensional (P2D) electrochemical model can give insight into the internal behavior of lithium-ion batteries, which is of great significance for intelligent battery management. However, the computational complexity of the P2D model greatly limits its onboard application. This paper devotes to develop a reduced-order electrochemical model (ROEM) with high fidelity yet low computational cost. First, for the simplification of the electrolyte diffusion process in batteries, domain decomposition technique is applied to divide the whole cell sandwich into two computation domains. The polynomial approximation method is adopted to describe the electrolyte concentration distribution in each domain, so that the electrolyte diffusion process is represented by two independent state variables. Next, combining the simplified electrolyte diffusion process and other dynamics in lithium-ion batteries, the complete ROEM is obtained as a five-state diagonal system. Finally, the prediction accuracy of the ROEM on electrolyte concentration, electrolyte diffusion overpotential and terminal voltage is verified by comparing with the P2D model and experimental results. Moreover, the proposed ROEM has an ideal computing speed for real-time application, which is at least 600 times faster than the rigorous P2D model.

A comparison of model prediction from P2D and particle packing with experiment

Design and optimization of the microstructure of the lithium-ion cell electrode is the key to improving its rate capability after the type and particle size of the active materials are fixed. The P2D electrochemical model, although widely-utilized, has limitation for this purpose due to its homogeneous description of the electrode particles and pores. Conversely, the particle packing model, which is capable of describing the spatial and size distributions of active particles, as well as the conductive network between them, offers new potential. In this work, for electrode designs with different areal/press densities, we compare the predictions from the P2D model and particle packing model with experiments. It is shown that the simulated rate discharge performance of the particle packing model fits well with the experimental tests, while the predictions of the P2D model show ambiguities and inadequacies at a high discharge rate (2C). Tortuosity, which is an important characteristic parameter of pore structure, has been investigated to correct the accuracy of P2D models, and the fitted values calculated from the particle packing model and experimental measurement are compared. In addition, we compare the difference of the lithium ion concentration distribution inside the electroactive particles and electrolytes between the P2D model (pseudo two-dimensional and homogeneous) and the particle packing model (two-dimensional and heterogeneous).

Comparative study of reduced-order electrochemical models of the lithium-ion battery

A reliable and efficient lithium-ion battery model is the basis of state estimation and fault diagnosis in the battery management system (BMS). The pseudo-two-dimensional (P2D) mechanism model represented by using partial differential equations has many parameters and high accuracy, but its calculation is time-consuming. The model order should be reduced for the on-board BMS. Here in this work, by using the same model parameters, the P2D model and the order-reduced models including the single particle model (SPM) and the lumped particle model (LPM) are built and their voltage accuracies and operation time are compared with each other. Based on the porous electrode model, the concentrated solution theory, and the assumption of uniform current of the battery, the current density is redistributed by the volume ratio of the solid phase to the liquid phase of the electrode. Furthermore, the overpotential and ohmic resistance caused by the lithium-ion concentration distribution in the liquid phase is deduced to offset the battery voltage bias under a large discharge rate. An unconstrained convex optimization method is established to optimize the concentration difference overpotential of the liquid phase of the P2D model battery, the optimized results of which are used to compensate for the LPM voltage.Under the conditions of the constant current discharge (CCD) of 0.1C — 4C at the ambient temperature, pulse discharge and dynamic stress test (DST), the electrical performance and the operation time of both the LPM and the SPM are compared to those of the P2D model. Some results are validated and given by the model simulation. Firstly, the accuracy of LPM is over 30% higher than those of the SPM at the CCD rates of 0.1 C, 0.5 C and 1 C, and about 30% worse than those of the SPM at the CCD rates of 2 C, 3 C, and 4 C. Secondly, the optimized LPM can produce a voltage in good approximation to the voltage of the P2D model with an absolute relative error of the model voltage below 1.5% whether it is caused by the CCD or the DST. Thirdly, the optimized LPM can run efficiently and the needed calculation time cuts down by 85% and 65% for the P2D and the SPM, respectively. For the real-time applications of lithium-ion batteries, the proposed compensation method by adding the overpotential in the liquid phase can make the LPM produce reliable voltage with shorter operation time than either the SPM or the P2D model.

Li-ion battery SOC estimation method using a Neural Network trained with data generated by a P2D model

Abstract The State Of Charge (SOC) estimation of a Li-ion battery is still an open problem. The most classical method, Coulomb Counting (CC) is vulnerable to current measurement bias. Measuring the Open-Circuit Voltage (OCV) allows to correct the error accumulated by the CC method, but only after the battery has been unsolicited long enough. Regarding these deficiencies, advanced SOC estimation methods try to combine current and voltage information, and are either based on an Extended Kalman Filter (EKF), which represents a certain algorithmic complexity and is hard to calibrate, or on black-box methods. In particular, methods using a Neural Network (NN) have been investigated in the literature, but take usually into account only instantaneous information, failing to represent the dynamic of ion diffusion in the electrodes. By considering also a close-past current integral as an input, this paper proposes a NN model able to correct initial SOC estimation errors and handle current measurement bias, and achieving a better estimation performance than a classical NN model taking only instantaneous information as an input.