Battery Cell Model Research Articles

Mathematical Model of Lithium-Ion Battery Cell and Battery (Lib) on its Basis

The article considers a mathematical model of lithium-ion battery cell and battery (LIB) on its basis. The developed mathematical model allows predicting LIB temperature on different parts of its surface during charging and discharging by nominal and maximum currents. The results of the battery discharge process simulation and validation of the mathematical model based on the field experiment results are also presented

Empirical Electrical and Degradation Model for Electric Vehicle Batteries

Battery degradation is one of the key barriers to the correct deployment of electric vehicle technology. Therefore, it is necessary to model, with sufficient precision, the State of Health (SoH) of batteries at every moment to know if they are useful as well as to develop operating strategies aimed at lifetime maximization. This paper presents a commercial electric vehicle with a nickel-cobalt-manganese (NCM) battery cell model that is composed of electrical and degradation submodels given by cycling aging. The studied cell is an LG Chem E63 cell, which is used in Renault Zoe electric vehicles. This degradation model is based on experimental results that are interpolated in the Hermite Cubic Interpolation Polynomial (PCHIP), with the exception of the number of cycles, whose impact is determined by a potential law. Temperature and C-rate are found to be the most influential factors in the aging of these batteries. The degradation model developed presents an RMSE of 1.12% in capacity fade and 2.63% in power fade. Furthermore, an application of the model is presented, in which high demanding (highway), average demanding (mixed), and low demanding (urban) driving environments are analyzed in terms of degradation.

Multi-Scale, Electro-Thermal Model of NMC Battery Cell

Battery models often either fail to deliver a complete picture of the physical phenomena occurring in the cell or fail to minimize computational effort. So far, the demand for a detailed internal thermal model of battery cells with a reasonable computation time has remained unanswered. This paper addresses such question introducing a multi-domain model whose accuracy makes it suitable for thermal management system development, at a lower computational cost than competing models. The approach features an equivalent circuit parameter model with chemistry-based parameters coupled with an internal heat transfer model. The internal heat transfer model includes different sections of the cell, addressing the anisotropy and the temperature-dependence of physical properties. Material properties are partly based on manufacturer's data sheet, partly taken from literature. The development software platform enables a sensible reduction of computational effort with respect to traditional modeling techniques. Results were validated against an aggressive current at different temperatures and against current profiles obtained from two different drive cycles at different ambient temperature. The model proves to be very good in terms of accuracy.

Ideal benefits of exceeding fixed voltage limits on lithium-ion batteries with increasing cycle age

This work quantifies what can safely be gained in terms of charged energy by disregarding conventional fixed limits on lithium-ion cell terminal voltage and instead placing limits on side reaction overpotential. A high-fidelity lithium-ion battery cell model is subjected to a range of constant currents given a set of initial states of charge (SoC). With limits placed on side reaction overpotential, it is possible to safely charge additional energy into the cell after the voltage limit has been reached. The effects of cell ageing through solid electrolyte interphase build-up are included in the model and both a fresh cell and a 4000 cycles aged cell are thereby investigated. It is shown that limiting anode plating overpotential instead of terminal voltage results in a theoretical additional 6% of total cell energy capacity charged for a fresh cell and 4% for an aged cell. Furthermore, with low enough initial SoC a 10C current is safe for five to ten seconds after exceeding the cell voltage limit depending on cell age. When evaluated on a city bus drive cycle, use of plating overpotential limits over voltage limits is shown to enable additional recovery of 2.5–14% of traction energy.

Adaptive Forgetting Factor Recursive Least Square Algorithm for Online Identification of Equivalent Circuit Model Parameters of a Lithium-Ion Battery

With the popularity of electric vehicles, lithium-ion batteries as a power source are an important part of electric vehicles, and online identification of equivalent circuit model parameters of a lithium-ion battery has gradually become a focus of research. A second-order RC equivalent circuit model of a lithium-ion battery cell is modeled and analyzed in this paper. An adaptive expression of the variable forgetting factor is constructed. An adaptive forgetting factor recursive least square (AFFRLS) method for online identification of equivalent circuit model parameters is proposed. The equivalent circuit model parameters are identified online on the basis of the dynamic stress testing (DST) experiment. The online voltage prediction of the lithium-ion battery is carried out by using the identified circuit parameters. Taking the measurable actual terminal voltage of a single battery cell as a reference, by comparing the predicted battery terminal voltage with the actual measured terminal voltage, it is shown that the proposed AFFRLS algorithm is superior to the existing forgetting factor recursive least square (FFRLS) and variable forgetting factor recursive least square (VFFRLS) algorithms in accuracy and rapidity, which proves the feasibility and correctness of the proposed parameter identification algorithm.

An Electrical Equivalent Circuit Model of a Lithium Titanate Oxide Battery

A precise lithium-ion battery model is required to specify their appropriateness for different applications and to study their dynamic behavior. In addition, it is important to design an efficient battery system for power applications. In this investigation, a second-order equivalent electrical circuit battery model, which is the most conventional method of characterizing the behavior of a lithium-ion battery, was developed. The current pulse procedure was employed for parameterization of the model. The construction of the model was described in detail, and a battery model for a 13 Ah lithium titanate oxide battery cell was demonstrated. Comprehensive characterization experiments were accomplished for an extensive range of operating situations. The outcomes were employed to parameterize the suggested dynamic model of the lithium titanate oxide battery cell. The simulation outcomes were compared to the laboratory measurements. In addition, the proposed lithium-ion battery model was validated. The recommended model was assessed, and the proposed model was able to anticipate precisely the current and voltage performance.

Research on vacuum drying process and internal heat conduction of Li-ion battery core

In this research, an innovative cylindrical automatic battery core oven was designed to avoid the structural deformation that frequently occurs in traditional ovens. The oven could be automatically connected with the electrolyte injection process after baking, achieving improvement in a battery's baking consistency. This contributed to the feasibility of studying the internal heat conduction process of batch battery cores during actual baking processes. A mathematical model of a certain plate battery cell during the baking process was established. The simulation results of the temperature change inside the battery core during the baking process were consistent with the calculation results of the mathematical model. The temperature distribution at each point inside the battery core could be fitted through the thermal conductivity at different temperatures and the temperature distribution between the layers of the battery core. Finally, based on the thermodynamic balance energy conservation method, the relationship between the temperature change inside the battery core and the entire baking process was established. A feasible algorithm for studying the thermal conduction of complex material and internal structure objects in the baking process was obtained.

Nonlinear Temperature-Dependent State Model of Cylindrical LiFePO4 Battery for Open-Circuit Voltage, Terminal Voltage and State-of-Charge Estimation with Extended Kalman Filter

Ambient temperature affects the performance of a battery power system and its accuracy in state-of-charge (SOC) estimation for electric vehicles and smart grid systems. This paper proposes a battery model that considered ambient temperature, cell temperature, hysteresis voltage and thermal aging on capacity due to multiple charging and discharging. The SOC is then estimated using an extended Kalman filter. Several forms of validation were tested on an actual cell battery under specific ambient temperatures to verify the battery cell model, terminal voltage and SOC estimation performance. The SOC estimation results show an improvement in root-mean-squared error as compared to Extended Kalman Filter (EKF) without considering the temperature dependency. The proposed battery temperature-dependent model gave a smaller root-mean square error in SOC and terminal voltage at 5 °C, 15 °C and 45 °C.

Zero dimensional dynamic model of vanadium redox flow battery cell incorporating all modes of vanadium ions crossover

A 0-D dynamic mathematical model for a single Vanadium Redox Flow Battery (VRFB) cell is proposed. The model is based on the conservation principles of charge and mass transfer focusing on the precise simulation of crossover with diffusion, migration and convection. The influence of these phenomena on the capacity decay was systematically analyzed, revealing considerable impact of convection component, which dominates under diffusion and migration and mainly responsible for observed capacity loss. The model allows to simulate main characteristics of VRFB systems (such as battery voltage, state of charge, charge/discharge time and capacity decay due to crossover) with high accuracy. The model was validated with experimental data in the wide range of current densities (40–100 mA cm−2), and the results demonstrated good agreement with experiments having an average error within 5% range. In addition, the model requires a modest computational time and power, and, therefore, it can be suitable for application in advanced control-monitoring tools, which are necessary for a long-service life and sustainable operation of VRFB systems.

Homogenized modeling methodology for 18650 lithium-ion battery module under large deformation.

Effective lithium-ion battery module modeling has become a bottleneck for full-size electric vehicle crash safety numerical simulation. Modeling every single cell in detail would be costly. However, computational accuracy could be lost if the module is modeled by using a simple bulk material or rigid body. To solve this critical engineering problem, a general method to establish a computational homogenized model for the cylindrical battery module is proposed. A single battery cell model is developed and validated through radial compression and bending experiments. To analyze the homogenized mechanical properties of the module, a representative unit cell (RUC) is extracted with the periodic boundary condition applied on it. An elastic–plastic constitutive model is established to describe the computational homogenized model for the module. Two typical packing modes, i.e., cubic dense packing and hexagonal packing for the homogenized equivalent battery module (EBM) model, are targeted for validation compression tests, as well as the models with detailed single cell description. Further, the homogenized EBM model is confirmed to agree reasonably well with the detailed battery module (DBM) model for different packing modes with a length scale of up to 15 × 15 cells and 12% deformation where the short circuit takes place. The suggested homogenized model for battery module makes way for battery module and pack safety evaluation for full-size electric vehicle crashworthiness analysis.

Systematic Derivation and Tuning of a Compact Differential-Algebraic Equations Model for LiFePO4-Graphite Li-Ion Batteries

This paper presents a procedure for deriving and tuning a compact differential-algebraic equation (DAE) model for the LiFePO4-graphite lithium-ion battery cell. A reduced order model can drastically decrease the simulation time with a minimal loss of the prediction accuracy for the Li-ion battery. This paper proposes a method for choosing a Galerkin formulation that will produce a compact and solvable DAE system from the original higher-order model of the Lithium-ion battery cell. Moreover, a systematic tuning of the model parameters using the global optimization method is demonstrated by exploiting the computational efficiency of the simplified model. When coupled with the model for describing the hysteresis of the battery cell, the tuned model, consisting of 24 DAEs, shows a good agreement with the experimental data from a LiFePO4-graphite battery cell at rates up to 4C.

Derivation and Tuning of a Compact Differential-Algebraic Equations Model for LiFePO4-Graphite Li-Ion Batteries

This paper presents a procedure for deriving and tuning a compact and solvable differential-algebraic equations (DAE) model for the LiFePO4-graphite battery cell. Electrochemical models of the battery cell are typically represented by complex partial differential equations of state variables and parameters whose relationships can be highly nonlinear. Several software packages are available for numerically solving these equations for simulations. However, their long computing time due to the complexity of the model is a major bottleneck for control and monitoring applications. A reduced order model (ROM) can drastically decrease the simulation time with a minimal loss of the prediction accuracy. A ROM is constructed by simplifying or approximating parameters of the full-order model of the battery cell. For on-line diagnostics and real-time control purposes, a lower-order compact representation of complicated transport and diffusion phenomena of a lithium-ion battery is highly desirable. In this paper, the psedo-2D (P2D) electrochemical model of the battery cell is simplified based on polynomial representations of pore-wall flux and lithium concentrations in a similar manner to previous studies. However, instead of adopting the standard Galerkin method which tends to increase the number of equations, this paper adopts Subramanian et al.’s method which demonstrated a potential for producing a compact description of a lithium-ion battery cell. While a traditional Galerkin method requires selecting particular polynomial representations which satisfy the boundary conditions, Subramanian et al.’s method selects a simple polynomial which can be analytically integrated foregoing setting up separate polynomials for solid and electrolyte potentials. This technique, therefore, has a potential to drastically reduce the size of simplified system. However, since the boundary conditions should be satisfied by additional analytical equations, one requires judicious choice of Galerkin formulations for electrolyte concentration in order to build a solvable DAE system. This paper introduces a systematic way of assessing a Galerkin formulation for the electrolyte concentration based on the theorem of Weierstrass. It is shown that each different Galerkin formulation converts the governing equation and its boundary conditions for the electrolyte concentration into a different set of linear DAE’s. However, not all DAE systems are solvable and some may induce numerical instabilities. It is shown that a full rank of the matrix pencil can ensure that a certain Galerkin formulation produces a solvable DAE system. Usefulness of the proposed method is illustrated by comparing several different Galerkin formulations for the LiFePO4-graphite system. In addition, this paper improves the accuracy of the model by accounting for the hysteresis of open-circuit voltage in LiFePO4 using a differential equation model. When the order of the polynomials are chosen at fours, the P2D model of the cell is simplified into a system of 24 DAE’s. This size is significantly smaller than those of comparable ROMs in the literature. The developed DAE system is solved by using SUNDIAL’s IDA solver where a typical charge/discharge cycle can be simulated under 10 seconds on a regular personal computer. The parameters of the developed DAE model are tuned based on charge/discharge experimental data from a commercial LiFePO4-graphite battery. In this paper, a systematic tuning of the model parameters is investigated by exploiting the fast simulation capability of the developed model. Based on a sensitivity study, six model parameters are chosen for tuning. These tuning parameters, thus selected, include the solid phase diffusivity of the negative electrode, initial hysteresis parameters, reaction rate constants, and the contact resistance. The genetic algorithm is applied to simultaneously find the six model parameters that minimize the sum of squared errors in charge/discharge voltages. The tuned model shows a good agreement with the experimental data at rates upto 4C. Contributions of this paper can be summarized as follows. This paper proposes a new method to ensure a compact DAE system is solvable when it is driven from the original higher-order model of the Lithium-ion battery cell. Moreover, a systematic tuning of the model parameters using the global optimization method is demonstrated by exploiting the computational efficiency of the simplified model. When coupled with the model for describing the hysteresis of the battery cell, the tuned model shows a good agreement with the experimental data from a LiFePO4-graphite battery cell.

FPGA-synthesizable Electrical Battery Cell Model for High Performance Real-time Algorithms

Modern battery management systems (BMS) for advanced battery energy storages are expected to provide sufficient and reliable State-of-Charge (SoC) and State-of-Health (SoH) information. Focusing also on mid- and long-term maintenance purposes, health monitoring can be realized only by using high performance real-time estimation algorithms involving online electrical battery cell model. Due to the nonlinear I-V characteristics of cells and multivariable nonlinear functions describing the model parameters, a real-time model synthesized to FPGA seems to be the best solution to fulfill also the strongest requirements of energy management and e-mobility applications in respect of scalability, modularity, accuracy and effectiveness. In this paper, an FPGA-synthesizable battery cell model is presented and proposed. The design approach is discussed from offline to online model design including the model considerations using MATLAB/Simulink ® . The performance analysis and evaluation referenced to the offline model are presented and discussed.

New Electro-Thermal Battery Pack Model of an Electric Vehicle

Since the evolution of the electric and hybrid vehicle, the analysis of batteries’ characteristics and influence on driving range has become essential. This fact advocates the necessity of accurate simulation modeling for batteries. Different models for the Li-ion battery cell are reviewed in this paper and a group of the highly dynamic models is selected for comparison. A new open circuit voltage (OCV) model is proposed. The new model can simulate the OCV curves of lithium iron magnesium phosphate (LiFeMgPO4) battery type at different temperatures. It also considers both charging and discharging cases. The most remarkable features from different models, in addition to the proposed OCV model, are integrated in a single hybrid electrical model. A lumped thermal model is implemented to simulate the temperature development in the battery cell. The synthesized electro-thermal battery cell model is extended to model a battery pack of an actual electric vehicle. Experimental tests on the battery, as well as drive tests on the vehicle are performed. The proposed model demonstrates a higher modeling accuracy, for the battery pack voltage, than the constituent models under extreme maneuver drive tests.

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

Lithium ion (li-ion) batteries are gradually increasing their volumetric power and energy densities due to requirements imposed by electric vehicles and portable electronics applications. In consequence, modern lithium ion battery cells and battery packs are having much more compact design where a high amount of energy is encapsulated in a small volume. This imposes a need for an accurate thermal modeling of li-ion batteries in order to avoid battery cells overheating, which leads to safety concerns (e.g. thermal runaways) and accelerates battery cell's performance degradation. Conventional methods for two- and three-dimensional thermal modeling of lithium ion batteries, usually require a coupled electrochemical battery cell model and a lot of knowledge about battery cell internal composition which are not provided and often protected by the battery cell’s manufacturers. This paper proposes an alternative method for battery cell 2D modeling based on the extended concept of electrothermal impedance spectroscopy. Moreover, a verification of the accuracy of the obtained results will be performed. Electrothermal impedance spectroscopy and proposed approach Barsoukov et al. were the first ones presenting the concept of electrothermal impedance spectroscopy (ETIS) in [1]. Later the concept was further extended and improved by Schmidt et al., by introducing internal heat excitation and a more accurate frequency-based measurement method [2]. ETIS is a non-destructive, relatively easy to implement, ‘entropy-free’ and not requiring any a priori knowledge about cell internal composition method, which is used for determining battery cell’s heat capacity and heat conductivity. The ETIS method is based on applying a specific heat flow to the battery and measuring the amplitude and phase delay of resulting battery temperature response [2]. For the frequency-based method, this procedure is repeated for several heat excitation frequencies and thus the thermal impedance function is defined. So far, the ETIS method has been used for one point measurements. This work is extendig the ETIS concept to multi-point measurements and study the accuracy of the two-dimensional thermal model parameterized by the means of the multi-point ETIS measurement. Laboratory setup and description of experiments A laboratory setup was built based on a high-bandwidth Kepco galvanostat and several high-precision temperature sensors located at different points of the high-power LiMO2/Li4Ti5O12 battery cell (Fig.1). Frequency-based method with internal heat generation was applied and results for two spots, on the battery cell surface, are presented in Fig.2. The obtained results are demonstrating different ‘local’ thermal impedances of the battery cell and in consequence uneven battery cell heating (Fig.3 ad Fig.4). These spot dependent thermal impedance functions can be used later for two-dimensional thermal modeling of battery cell by means e.g. Cauer model [3]. Final version of the paper In the final version of the paper, the detailed results from multi-point ETIS will be presented and discussed. A two-dimensional equivalent thermal circuit based battery model will be developed and parametrized by means of multi-point ETIS. Finally, the accuracy of this two-dimensional battery thermal model [3], developed based on the multi-point ETIS, will be analyzed.

Dynamic battery cell model and state of charge estimation

Mathematical modelling and the dynamic simulation of battery storage systems can be challenging and demanding due to the nonlinear nature of the battery chemistry. This paper introduces a new dynamic battery model, with application to state of charge estimation, considering all possible aspects of environmental conditions and variables. The aim of this paper is to present a suitable convenient, generic dynamic representation of rechargeable battery dynamics that can be used to model any Lithium-ion rechargeable battery. The proposed representation is used to develop a dynamic model considering the thermal balance of heat generation mechanism of the battery cell and the ambient temperature effect including other variables such as storage effects, cyclic charging, battery internal resistance, state of charge etc. The results of the simulations have been used to study the characteristics of a Lithium-ion battery and the proposed battery model is shown to produce responses within 98% of known experimental measurements.

Dynamical modeling of Li-ion batteries for electric vehicle applications based on hybrid Particle Swarm–Nelder–Mead (PSO–NM) optimization algorithm

In recent years, Li-ion batteries are widely used in various applications, such as electric and hybrid vehicles application. Their higher specific power and energy density, high cycle lifetime and decreasing costs have made them an attractive and alternative energy storage technology to lead-acid or nickel-metal hydride batteries in embedded power supplies. In the present work, the electric modeling of a Li-ion battery cell in real operation conditions imposed by an electric vehicle application is carried out. A dynamic equivalent circuit model has been used to simulate several electrochemical processes occurring in a commercially available 40 Ah Li-ion battery cell with NMC cathode material and graphitic anode. The model is parameterized with measurement data in time-domain using a hybrid Particle Swarm–Nelder–Mead (PSO–NM) optimization algorithm. This last one is used to solve the parameters identification problem of Li-ion battery model.The developed model of Li-ion battery cell has been validated on real driving cycle provided by an urban electric vehicle. Obtained results show that there is a good match between experiment and simulation results with a maximum modeling error less than 0.5%, which proves the well performance of our model and confirms the interest of a hybrid (PSO–NM) optimization algorithm for battery identification parameters.

전기 자동차 가상 플랫폼용 배터리 모델 개발 및 검증

In this paper, a battery model for electric vehicle virtual platform was developed. A battery model consisted of a battery cell model and battery thermal management system. A battery cell model was developed based on Randles equivalent circuit model. Circuit parameters in the form of 3D map data was obtained by charge-discharge experiment of Li-Polymer battery in various temperature condition. The developed battery cell model was experimentally verified by comparing voltages. Thermal management system model was also developed using heat generator, heat transfer and convection model, and cooling fan. For verification of the developed battery model in vehicle level, the integrated battery model was applied in to EV(electric vehicle) virtual platform, and virtual driving simulation using UDDS velocity profile was conducted. The accuracy of the developed battery model has been verified by comparing the simulation results from EV platform with the experimental data.

Nonlinear Adaptive Observer for a Lithium-Ion Battery Cell Based on Coupled Electrochemical–Thermal Model

Real-time estimation of battery internal states and physical parameters is of the utmost importance for intelligent battery management systems (BMS). Electrochemical models, derived from the principles of electrochemistry, are arguably more accurate in capturing the physical mechanism of the battery cells than their counterpart data-driven or equivalent circuit models (ECM). Moreover, the electrochemical phenomena inside the battery cells are coupled with the thermal dynamics of the cells. Therefore, consideration of the coupling between electrochemical and thermal dynamics inside the battery cell can be potentially advantageous for improving the accuracy of the estimation. In this paper, a nonlinear adaptive observer scheme is developed based on a coupled electrochemical–thermal model of a Li-ion battery cell. The proposed adaptive observer scheme estimates the distributed Li-ion concentration and temperature states inside the electrode, and some of the electrochemical model parameters, simultaneously. These states and parameters determine the state of charge (SOC) and state of health (SOH) of the battery cell. The adaptive scheme is split into two separate but coupled observers, which simplifies the design and gain tuning procedures. The design relies on a Lyapunov's stability analysis of the observers, which guarantees the convergence of the combined state-parameter estimates. To validate the effectiveness of the scheme, both simulation and experimental studies are performed. The results show that the adaptive scheme is able to estimate the desired variables with reasonable accuracy. Finally, some scenarios are described where the performance of the scheme degrades.

Influence of connecting plate resistance upon LiFePO4 battery performance

Abstract The primary challenge to the commercialization of any electric vehicle is the performance management of the battery pack. The performance of the battery module is influenced by the resistance of the inter-cell connecting plates (ICCP) and the position of the battery module posts (BMP). A new battery cell model based on the Matlab–Simscape platform is developed and validated using a constant current discharge test and a pulse discharge test. Taken the ICCP as resistors, a parallel-connected battery module model (PCBMM) is established based on the battery cell model. The effect of inter-cell connecting plate resistance (ICCPR) on the battery module performance is simulated. Simulation results indicate that the ICCPR causes unevenly current flow among the battery cells. The battery cell directly connected to the BMP is the first one reaching its end-of-discharge (EOD) voltage. Also, it presents the lowest terminal voltage and state of charge (SOC) during the discharge process. The battery cell directly connected to the BMP goes into deep discharge state more easily. Therefore, it performs higher aging rate. The aging of the battery cell causes over-discharge of the adjacent battery cells. The reasonable ratio of the ICCPR to the battery ohmic internal resistance (OIR) is discussed for different average currents and different numbers of battery cells, to guarantee the maximum SOC evaluation error within a target value of 0.05.