Electrochemical Model Of Lithium-ion Battery Research Articles

A Time-Adaptive Order Reduction Technique for the Doyle-Fuller-Newman Electrochemical Model of Lithium-Ion Batteries

A time-adaptive reduced order model (ROM) is developed for the electrochemical model for lithium-ion cells derived by Doyle, Fuller, and Newman (DFN) [M. Doyle, T. F. Fuller and J. Newman, J. Electrochem. Soc., 140 1526 (1993)]. The main advantage of a time-adaptive strategy is that it does not require a set of full order model simulations to be generated beforehand and, thus, it is the most cost-effective alternative when no databases are available. However, the reduction of this electrochemical problem exhibits special features that require ad hoc solutions, preventing the application of generic strategies. This complexity is carefully analysed, focusing on mode selection, treatment of non-linearities and error estimation. Despite of all this analysis being done for a pseudo-two-dimensional DFN model, we show that such complexity is intrinsic to the physics of the electrochemical problem, making the analysis applicable to a pseudo-four-dimensional DFN model, where results prove that the benefits of a reduction in the number of degrees of freedom are more self-evident. The efficiency, robustness and accuracy of our method are remarkable, as shown by the macroscopic (cell voltage) and internal (variable distributions) results obtained from the simulation of two different electrochemical cells under several charge/discharge C-rates.

A simplified electro-chemical lithium-ion battery model applicable for in situ monitoring and online control

The penetration of lithium-ion batteries (LIBs) in transport, energy, and communication systems is increasing rapidly. A meticulous but simplified LIB model for non-uniform internal state monitoring and online control is sought in practice. Based on the pseudo-two-dimensional (P2D) model, a simplified electro-chemical model for LIBs is proposed. Specifically, a rigorous model of the non-uniform reaction rates inside the battery is derived. Sub-models that capture the non-uniformity of current densities, potentials and concentrations are developed synchronously. Time-variant parameters and a lumped thermal model are incorporated as well. A full-cycle simulation framework, including the discretization, initialization, stabilization and closed-loop correction methods, is designed for ease of online control. Numerical experiments on the widely used NCM and LFP 18650 batteries under standard charge and discharge protocols and dynamic protocols during the peak-shaving or regulation service are conducted for validation. Generally, the speed of the proposed model increases hundreds of times compared to the P2D model. The estimation accuracy of internal and external states increases around 10% to 100% compared to state-of-art electro-chemical models. In addition, the correction speed and accuracy of the closed-loop framework increase around ten times and around 100% respectively compared to the widely used ensemble Kalman filter.

A fractional-order model of lithium-ion battery considering polarization in electrolyte and thermal effect

With the growing demand of safety and accurate control for electric vehicles, it is urgent to develop a physics-based electrochemical model of lithium-ion battery with simple calculation and high accuracy over wide temperature range for application in battery management system (BMS). However, traditional electrochemical models are too complex to be applied in real usage, and most of them fail to capture thermal characteristics of the cell. Therefore, a fractional-order model of lithium-ion battery considering polarization in electrolyte and thermal effect (FOMeT) is proposed in this paper. The fractional-order model (FOM) is improved by considering the polarization in electrolyte. The particle thermal model is proposed to describe the heat generation and absorption of the cell. Finally, the FOM considering electrolyte polarization and the particle thermal model are combined to form FOMeT by coupling the cell temperature and dynamics of lithium-ion. The results show that the proposed model performs high voltage accuracy and temperature accuracy over wide temperature range (273.15K∼318.15K) and wide current load range (0.5C∼2C).

Enhancing the LCO 18,650 Battery Charging/Discharging Using Temperature and Electrical Based Model

Lithium-ion batteries are commonly used in electric vehicles, embedded systems, and portable devices, including laptops and mobile phones. Electrochemical models are widely used in battery diagnostics and charging/discharging control, considering their high extractability and physical interpretability. Many artificial intelligence charging algorithms also use electrochemical models for to enhance operation efficiency and maintain a higher state of health. However, the parameter identification of electrochemical models is challenging due to the complicated model structure and the high count of physical parameters to be considered. In this manuscript, a comprehensive electrochemical lithium-ion battery model is proposed for the charging and discharging processes. The proposed model accounts for all dynamic characteristics of the battery, including the cell open-circuit voltage, cell voltage, internal battery impedance, charging/discharging current, and temperature. The key novelty of the proposed model is the use of simulated open-circuit voltage and simulated changes in entropy data instead of experimental data to provide battery voltage and temperature profiles during charging and discharging cycles in the development of the final model. An available experimental dataset at NASA for an LCO 18,650 battery was utilized to test the proposed model. The mean absolute error for the simulated charging cell voltage and temperature values were 0.05 V and 0.3 °C, compared with 0.14 V and 0.65 °C for the discharging profile. The simulation results proved the effectiveness and accuracy of the proposed model, while simplicity was the key factor in developing the final model, as shown in the subsequent sections of the manuscript.

Understanding the effects of diffusion coefficient and exchange current density on the electrochemical model of lithium-ion batteries

The diffusion coefficient and exchange current density are the two dominant parameters that determine the electrochemical characteristics of the electrochemical battery model. Nevertheless, both parameter values are generally adopted from well-known literature or experimental data measured under limited conditions and are sometimes overfitted to match actual electrochemical behaviors without full consideration. Herein, the diffusion coefficients and exchange current densities of a LiNi0·4Mn0·3Co0·3O2/Li cell are measured and applied to the electrochemical model (based on Newman's model) using four different electrochemical methods: galvanostatic intermittent titration technique (GITT), potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS), and cyclic voltammetry (CV). Without any fitting, the model adopting the diffusion coefficient and exchange current density measured from PITT and EIS, respectively, simulates the actual voltage–capacity profiles well. Thus, this case study provides a valuable opportunity to understand the advantages and disadvantages of each measurement method in obtaining key experimental parameters for electrochemical battery models.

Multi-scale design optimization of electric vehicles by analytical target cascading: From battery cell level to marketing level

The trend of vehicle electrification is rapidly growing and is likely to continue in the future. However, electric vehicles (EVs) with high vehicle performance, energy efficiency, and low cost are required to satisfy industry and customer needs. Design optimization is an important method that can significantly improve the performance of batteries and EVs. However, only a few studies integrate accurate full-order electrochemical models of lithium-ion batteries into optimization frameworks of the battery module, pack, and EV design owing to complex modeling with huge computational costs. Multi-scale models with high efficiency and accuracy are required to provide optimal design, considering the overall system across scales. This study develops an efficient multi-scale design optimization framework for EVs, including four levels from the battery cell level to the marketing level. In the engineering domain, three levels of fundamental physics-based models are developed—an electrochemical cell, thermal module, and EV dynamics—to describe the performance of EVs. In the marketing domain, a utility model is used to maximize profit while considering customer preferences and costs. In addition, the vehicle model at the top level of the engineering domain is linked with the marketing model. Thus, all four model levels are hierarchically connected and can pass information.The multi-scale design optimization problem is solved by applying an analytical target cascading (ATC) method specialized for multi-level optimization. Through the ATC framework, optimization problems at each level can be independently solved while satisfying the targets from upper levels. Results show that each level successfully communicates with the others and carries out optimization to maximize profit while satisfying various constraints. ATC reduces the computational cost by 3% compared to the conventional all-in-one (AIO) approach. Parametric studies provide insights into how these design parameters, constraints, and operating conditions affect each other. To the best of our knowledge, this study is the first attempt toward developing multi-scale level modeling of EVs, which covers the marketing (very high business level) down to the cell (very detailed engineering level) while satisfying multi-level safety constraints.

Approximate Solutions for Determining Electrolyte Concentrations in Electrochemical Models of Lithium-Ion Batteries

The pseudo two-dimensional (P2D) model and its reduced order models, such as the single particle model (SPM), are widely used in electrochemical modeling and simulating lithium-ion batteries. Although the SPM has a low computational burden, its accuracy is poor under high-rate discharge conditions. Therefore, to balance accuracy and efficiency, the SPM with one-dimensional spatial electrolyte dynamics (SPMe) has been proposed. However, due to the complex diffusion equations for electrolyte dynamics, calculating the lithium-ion concentration in the electrolyte is still difficult. Therefore, we propose the cosine approximation (CA) method to efficiently calculate lithium-ion concentrations. We first use the Laplace transform to analytically solve the diffusion equations, and then, the complete transfer function from the discharge rate to lithium-ion concentration is obtained. In addition, the proposed method is obtained by both truncating the time-domain analytical solution of an infinite series and using error compensation. Moreover, compared to the finite volume method, the new method is verified under the galvanostatic and dynamic profiles, where the higher the order of the method, the higher the accuracy. Finally, the second-order CA shows a higher degree of accuracy compared to the widely used second-order polynomial approximation.

Development and parameterization of a control-oriented electrochemical model of lithium-ion batteries for battery-management-systems applications

A precise electrochemical battery model is critical for advanced battery management systems to improve the safety and efficiency of electric vehicles. This paper presents a novel methodology to develop and parameterize the electrochemical model through cell teardown and current/voltage data estimation. The partial differential equations of ionic electrolyte and potential dynamics in the solid and liquid phases are solved and reduced to a low-order system with Padé approximation. The systematic identification procedure is proposed by first dividing the parameters into fixed geometric properties, thermodynamics, and kinetics. Then the cells are dismantled. Subsequent chemical and thermodynamic analyses, including half-cell tests, are conducted for parameter extraction. Next, the parameterized model is validated with extensive experimental data, illustrating the superior capability of predicting cell voltage with root-mean-square errors of 8.90 mV at 2C and 13.98 mV for Urban Dynamometer Driving Schedule profile at 0 °C. The accuracy of the cell internal electrochemical states of the reduced model is verified as well. Comparative studies concerning model accuracy and computation efficiency on hardware reveal that the model is 31% more accurate than equivalent circuit models but occupies similar computation resources. Finally, the need and advantages of combining cell teardown and parameter estimation in achieving a precise electrochemical model are addressed.

A new method to solve electrolyte diffusion equations for single particle model of lithium-ion batteries

It is one of basic tasks to solve the electrochemical model of lithium-ion batteries for obtaining the lithium-ion concentration in the electrolyte. In order to balance the computational efficiency and electrolyte dynamic property, it is assumed that reactions occur only at interfaces between the collector and the electrolyte. Based on the analytical solution to the liquid diffusion equations, which is in the form of infinite series, a new method is proposed to solve it. Under galvanostatic profiles, the analytic solution is an infinite time series transformed into a converged sum function by using the monotone convergence theorem. Under the dynamic profiles, the infinite series solution is simplified into an infinite discrete convolution of both the input and the sum function. The sum function is truncated by its characteristic of monotonic decay approaching to zero over time, thus obtaining a finite discrete convolution algorithm. Reference to the results from a professional finite element analysis software, the proposed algorithm can produce high accuracy with less computation time under both galvanostatic profiles and dynamic profiles. Also, there is only one parameter to be configured. Therefore, our algorithm will reduce the computation burden of the electrochemical model applied to a real-time battery management system.

Global Optimal Experiment Design for Li-Ion Batteries

We propose a method that enables the design of parameter specific optimal experiments to complement existing parametrization approaches. Previous studies on optimal experiments focus on fisher information based experiment design [1][2], which employ local sensitivities to characterize experiment information content. This has the distinct weakness of dependency on the initial parameter vector. We propose a method utilizing a global sensitivity scheme to fully map the available parameter space and thus account for model non-linearity and parameter interdependence. Furthermore, common optimal experiment design approaches for physics-based battery models consider a limited experiment space, choosing from a set a pre-defined experiments [2]. We circumvent this issue by algorithmically generating virtual experiments and finding the optimal one within this space. We validate our approach using both model and experiments. The experimental validation is based on the comparison with conventional battery characterization tools such as electrochemical impedance spectroscopy (EIS), galvanostatic intermittent titration technique (GITT) or scanning electron microscopy (SEM).With the accelerating growth in battery electric vehicles (BEV), efficient utilization of rapidly evolving system designs and chemistries shifts into focus. Recent developments towards nickel-rich cathode materials aiming for higher energy densities can only be an intermediate step towards the next generation of batteries. These fast paced improvements pose an immense challenge for the conventional approach to battery management systems (BMS), mainly in their reliance on empirical and experimentally validated control oriented models. Trends are pointing towards physics based (PM) as well as data-driven models (DM) for BMS, whose accuracy and resolution enables aging sensitive control. PM rely on long term cycling studies and detailed electrochemical characterization procedures for accurate parametrization.We propose a method for model parametrization utilizing global sensitivity based optimal experiment design. The method improves on conventional techniques in four ways: firstly, it significantly reduces computational and experimental effort, as we show by studying the impact of test length on identifiability. Secondly, it improves model accuracy through reductions in parameter error. Thirdly, it improves model fidelity by specifically designing experiments to excite desired parameters and finally, it enables full-cell parametrization with small experimental effort. We propose several use-cases for this method: beginning of life (BOL) parametrization, aging-specific experiments and model reparametrization and finally virtual twin [3] parametrization using a DM surrogate. We investigate which qualitatively dependent parameters can be untangled and therefore accurately determined from full cell measurements. We benchmark our method with half-cell experiments of nickel-rich electrodes harvested at beginning of life from commercial cells.[1] A. Pozzi, G. Ciaramella, S. Volkwein, and D. M. Raimondo, “Optimal design of experiments for a lithium-ion cell: Parameters identification of an isothermal single particle model with electrolyte dynamics,” en, Industrial & Engineering Chemistry Research, vol. 58, no. 3, pp. 1286–1299, 2019[2] S. Park, D. Kato, Z. Gima, R. Klein, and S. Moura, “Optimal Experimental Design for Parameterization of an Electrochemical Lithium-Ion Battery Model,”, Journal of The Electrochemical Society, vol. 165, no. 7, A1309–A1323, 2018[3] B. Wu, W. D. Widanage, S. Yang, and X. Liu, “Battery digital twins: Perspectives on the fusion of models, data and artificial intelligence for smart battery management systems,”, Energy and AI, vol. 1, 2020 Figure 1

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.

Implementation and evaluation of a practical electrochemical- thermal model of lithium-ion batteries for EV battery management system

To realize the electrochemical-thermal model in the battery management system (BMS), a control-oriented electrochemical model of lithium-ion batteries and its real-time implementation in the BMS of an electric vehicle (EV) are presented in this paper. Firstly, the improved pseudo-two-dimensional electrochemical model is derived to obtain the transfer function between the cell voltage and current by simplifying the partial differential equations with the Laplace transform, Pade approximation, etc. The temperature-sensitive parameters are identified at different temperatures to obtain the model temperature dependency. Then these temperature-dependent parameters are extracted for model decoupling. The presented model is validated to achieve high accuracy over a wide range of state-of-charges and temperatures with offline data. The root-mean-square (RMS) error in the prediction of terminal voltage could be limited within 28 mV when temperature decreases to −10 °C. Finally, the model is discretized and embedded into the targeted algorithm framework in the BMS of an EV to verify its effectiveness in real-time. The RMS error of the online estimated voltage is less than 15.8 mV under realistic city driving conditions at −13 °C, indicating the feasibility of the developed electrochemical model for broader EV applications.

Evaluation and observability analysis of an improved reduced-order electrochemical model for lithium-ion battery

The accurate modeling of lithium-ion battery is helpful for deserves developing advanced battery management system (BMS) and monitoring battery states. Despite the electrochemical model (EM) of a battery cell has gradually become a main candidate for advanced BMS, the EM-based estimators still face a big problem regarding to the weak observability. To address this issue, this paper proposes an improved reduced-order electrochemical model (iROEM) with guaranteed observability. First, the solid phase equations are reconstructed by combing Padé approximation and polynomial fitting method, and the electrolyte concentration equations are reduced by using volume averaging technique, which ultimately contributes the development of the iROEM. Second, the observability analysis of the proposed iROEM is conducted to facilitate the control applications in BMS. Finally, the designed iROEM is evaluated by performing a comparative study of the electrolyte concentration distributions and battery terminal voltages with respect to the pseudo two-dimensional model under the constant current and dynamic working conditions. The results demonstrate that the iROEM with guaranteed observability has high model fidelity and less computational complexity, which contributes to the resultant estimators for the lithium-ion battery electrochemical model.

State Estimation for Lithium-Ion Batteries With Phase Transition Materials Via Boundary Observers

Abstract Lithium iron phosphate (LiFePO4 or LFP) is a common active material in lithium-ion batteries. It has been observed that this material undergoes phase transitions during the normal charge and discharge operation of the battery. Electrochemical models of lithium-ion batteries can be modified to account for this phenomenon at the expense of some added complexity. We explore this problem for the single particle model (SPM) where the underlying dynamic model for diffusion of lithium ions in phase transition materials is a partial differential equation (PDE) with a moving boundary. We derive a novel boundary observer to estimate the concentration of lithium ions together with a moving boundary radius from the SPM via the backstepping method for PDEs, and simulations are provided to illustrate the performance of the observer. Our comments are stated on the gap between the proposed observer and a complete state-of-charge (SoC) estimation algorithm for lithium-ion batteries with phase transition materials.

Thermal component for an electrochemical lithium-Ion battery model: Impact and variation on the battery performance

Different battery chemistry gives different characteristics; however, these differences are gauged by the battery temperature through the Arrhenius law. A battery model is essential to predict and acts as a tool for analyzing the performance of a battery in the design stage, particularly for a battery pack design. The complexity of the battery model merely lies on the electrochemical part in which all of the diffusion, electron and charge transfer are modelled. On the other hand, the thermal component of the battery model is essential, allowing the temperature to have a direct impact on the battery performance. This paper compares and evaluates the impact of having different thermal component as a coupling to an electrochemical battery model. Concerning the electrochemical model, the thermal models are typically described based on the degree of its dimensionality. The highest degree of thermal model is a 3D-thermal model in which it maps the whole geometry of the battery. Nevertheless, we show that, having relatively higher degree of thermal model does not yield significant performance differences as compared to battery model that adopts a zero-dimensional thermal model. Adding a more complex thermal model only puts additional computational effort which extends the duration of the calculation. This suggests that the key integration of the thermal component to an electrochemical model is on the battery thermal-electrical interplay. The direction of the internal battery current during charge/discharge must be known or assumed before an appropriate thermal model is chosen. Increasing the dimensionality of the thermal model will be meaningless if the current density is not being feedback to the thermal model.

Optimal Sensor Selection for an Electrochemical Li-Ion Battery Model

This work rigorously evaluates which sensor combinations are best for estimating lithium-ion battery internal states related to state-of-charge, state-of-power, and state-of-health. Lithium-ion batteries have emerged as an enabling technology for many industries that seek the benefits of electrification such as automotive, power systems, and consumer electronics. Central to the operation of lithium-ion battery technology is the battery management system (BMS), whose role is to monitor the status of and facilitate the charging and discharging behavior of the system. Fundamentally, the core challenges of a BMS are modeling, estimation, and control problems. To date, the vast majority of BMS technology and research operates based on the assumption of what is currently possible to measure in a battery system: current, voltage, and temperature. However, valuable advanced BMS capabilities have proven to be challenging to develop based on this sensor limitation.To systematically evaluate the value of different sensing technologies in BMS's, we formulate the sensor selection problem. In other research domains, the sensor selection problem is motivated by the goal of maximizing the usefulness of available sensor data for a given estimation or controls goal [1-3]. The research here examines the sensor selection problem from a mathematical point-of-view without limiting ourselves to the practicality of the sensing technology. That is, instead of asking if some existing sensing technology improves state observability, we ask what sensors are theoretically best for estimating internal states. We seek to motivate the pursuit of new sensing technologies or more rigorously justify the use of existing sensing technologies.We first present a methodology for evaluating the impact of different potential novel sensing capabilities based on an observability analysis for a reduced-order electrochemical lithium-ion battery model, specifically, the Single Particle Model with Thermal Dynamics (SPM+T) [4-5]. We demonstrate the impact of incorporating different sensors on observability of the reduced-order electrochemical model. We find that the inclusion of certain sensors has a greater impact on model observability than others. The result in Figure 1 for the SPM+T model proves that voltage and surface temperature sensing is, in fact, best for state observability. However, this result may change for more complex models, such as the SPMeT [6-7] or others that incorporate additional dynamics such as multiple materials, stress mechanics, etc.

Electrochemical model of lithium-ion battery for wide frequency range applications

The electrochemical model is widely studied because of its capability to accurately describe various reactions inside the lithium-ion battery. In this paper, the impedance from 10 mHz to 1 kHz of the Pseudo 2-Dimensional (P2D) model is analyzed, and it is found that the impedance characteristics of the P2D model only at low frequencies (below 0.5 Hz) are consistent with those of actual batteries. In order to improve the applicability of the electrochemical model, a model with good simulation accuracy under the excitation of 10 mHz to 1 kHz is established, by combining the P2D model with the theory of the double layer (DL) and the solid electrolyte interphase (SEI). In the frequency domain, the new model is decoupled, the separate impedance characteristic of each component described by the model is analyzed, and the contribution of each component to the total impedance characteristics at each frequency band is analyzed and described in detail. Meanwhile, the impedance of the new model under the excitation of 10 mHz to 1 kHz is compared with the EIS data of the actual lithium-ion batteries to verify the simulation accuracy of the impedance of the new model under all frequencies. In the time domain, the responses of the new model and the P2D model at different conditions are compared with measured datas, and the results shows that the new model is superior to the P2D model under high-frequency excitation and has good simulation accuracy over a wide frequency range (10 mHz–1 kHz).

1D electrochemical model of lithium-ion battery for a sizing methodology of thermal power plant integrated storage system

The interest of using storage system has been investigated by grid operators over the past decades. Currently, some power plant manufacturers propose to integrate the storage system into thermal plants to meet grid codes requirements and improve the plant operability. Thermal powerplants change the way of the generation becoming peaking or cycling unit instead of baseload unit as few decades ago. This change of grid operability compels the power plant operators to enhance their flexibility, emission and efficiency. Storage systems seem to be a promising solution that can help achieve this change. Regarding the cost, it is mainly driven by the battery elements (a third of the total cost). Therefore, an oversizing of the solution will decrease the economic benefits. This article proposes a new electrochemical model of Li-ion battery implemented in a sizing methodology to enhance the business case. This method will also include asset losses, battery aging model and plant profiles. The new electrical model is based on the single particle and single electrode. It mainly focuses on the energy aspect and it exhibits good accuracy for the study purpose. Moreover, it has a simplified configuration using only supplier datasheet which logically leads to loss of accuracy. The model assessment is achieved by several battery technologies (Lithium Titanate Oxide, Lithium Iron Phosphate and Nickel Manganese Cobalt) and shows its use restrictions. At last, different plant profiles are run to show the benefits of the proposed approach.

Real-Time Parameter Estimation of an Electrochemical Lithium-Ion Battery Model Using a Long Short-Term Memory Network

An electrochemical lithium-ion battery model is well known to be suited for effectively describing the microstructure evolution in charging and discharging processes of a lithium-ion battery with practically realizable complexity. This paper presents a neural network-based parameter estimation scheme to identify the parameters of an electrochemical lithium-ion battery model in a near-optimal and real-time manner in order to consistently observe the electrochemical states of batteries. The network is first trained to learn the dynamics of the electrochemical lithium-ion battery model, and then, it is applied to estimate the parameters with available finite-time measurements of voltage, current, temperature, and state of charge. In order to efficiently learn the dynamic characteristics of a lithium-ion battery, a well-known recurrent neural network, called a long short-term memory model, is employed with other techniques such as batch normalization, dropout, and stochastic gradient descent with warm restarts for learning speed enhancement and regularization. Using synthetic and experimental data, we show that the proposed estimation scheme works well, finding parameters and recovering the voltage profiles within the root-mean-square error of 0.43% and 26 mV, respectively, even with measurements obtained within a sufficiently short interval of time.

A control-oriented electrochemical model for lithium-ion battery. Part II: Parameter identification based on reference electrode

Abstract Although electrochemical models have superior capabilities of internal states estimation to equivalent-circuit models, they have larger numbers of parameter values to be determined while predicting the behaviors of a real cell. Parameter identification of electrochemical models is essential but present methods are time-consuming and complex. In the “Part1” paper in this series, a lumped-parameter electrochemical model was built with the redundant/unobservable parameters removed. Using the this model, this paper proposes a novel stepwise method that can identify the whole set of parameter values for a physical cell using simple tests. The lumped-parameter model is specifically reformulated mostly based on frequency decomposition, and a reference electrode is included in the model to achieve electrode decoupling. The method is decomposed into four tests and eight steps, where the number of parameters to be identified in each step is significantly reduced, enhancing the computational efficiency and improving the identification accuracy. The identified values are first directly compared to the true values, and then the time-domain predictions of the lumped-parameter model using the identified values are compared to those of the full-order model using the true parameter values in terms of the terminal voltage and electrochemical states under different operation conditions.