Parameters Of Electrochemical Model Research Articles

Aging-Sensitive Fast-Charging for Heavy-Duty Electric Vehicles

To use lithium-ion cells on-board electric vehicles (EVs) safely and efficiently, a battery management system (BMS) is essential. It monitors the battery’s states and controls utilization by limiting e.g., current and temperature. Advanced BMS increasingly use electrochemical models to assess internal states of battery cells and apply usage constraints based on these [1]. The performance of an electrochemical BMS is closely tied to the performance of the underlying model and the accuracy of its parameters [2]. We employ a novel re-parametrization method to update electrochemically constrained optimal fast-charging procedure to minimize battery degradation. The parameters of electrochemical models are typically identified through a combination of physico-chemical characterization techniques and curve fitting [3]. Since model parameters change with aging [4], there is a need to re-parametrize electrochemical models on-board to conserve model accuracy. As basis for this re-parametrization, we propose a novel reference performance test that can be incorporated into a conventional over-night charge and performed intermittently.Optimal control has previously been demonstrated for fast-charging in EV applications [1]. However, electrochemical, and mechanical degradation need to be considered to allow optimal fast charging throughout batteries’ lifetimes. Khalik et al. [5] demonstrated how a charging procedure could be designed a-priori for the entire cycle life, considering a direct implementation of the solid-electrolyte-interphase growth and capacity fade due to the associated lithium consumption. Such approaches can extend battery lifetime, but neither yield optimal charging-procedures at every state-of-health nor handle unknown aging modes on the fly. Our proposed approach involves intermittent identification of electrochemical model parameters and subsequent update of the fast-charging protocol such that it adheres to electrochemical constraints throughout the entire battery lifetime.In this work, summarized in Figure 1, we present this methodology and show results from an experimental study testing the proposed approach vs. conventional charging procedures. The experimental study is performed on state-of-the art automotive cells used in heavy-duty electric vehicles.Figure caption: Comparison of a conventional electrochemically constrained fast-charging procedure with the aging-sensitive approach proposed in the present work.

Diagnosis and prognosis of battery degradation through re-evaluation and Gaussian process regression of electrochemical model parameters

Lithium-ion battery degradation is complex, and many mechanisms occur concurrently. In-depth degradation is traditionally investigated by post-mortem characterization in lab-settings. If mechanisms could instead be identified in-operando, utilization could be adjusted, and battery lifetime extended. We investigate changes in electrochemical model parameters during battery testing and their correlation with degradation observed in a traditional post-mortem characterization. Commercial batteries are cycle-aged using different stationary storage service cycles and a novel reference performance test is applied intermittently. This test is based on current profiles optimally designed with respect to maximized sensitivity for individual electrochemical parameters and embedded within a charging procedure. Usage dependency of parameter trajectories over the course of ageing is demonstrated and coupled to observed micro-structural changes. Subsequently, the parameter trajectories are extrapolated using Gaussian Process Regression for physics-based state-of-health estimation and remaining-useful-life prediction. We demonstrate and validate estimation of full cell performance under constant load at a later state in life.

Model Based Comparative Analysis of GDC and YSZ Based Solid Oxide Fuel Cells

Designing solid oxide fuel cell (SOFCs) stacks for transportation applications places new challenges on SOFC architecture and operation with respect to power density, dynamic response, and thermal management. Recent developments in SOFCs with either thin-film yttria stabilized zirconia (YSZ) electrolytes (thickness ≤ 5 μm) or highly conductive, gadolinia-doped ceria (GDC) electrolytes (thicknesses ≥10 μm) enable thigh-power-density stack operation at inlet temperatures well below 700ºC with the potential for using compliant seals and lower cost ferrous interconnect materials. Applications, such as hybridized aircraft engines, can use such SOFC stacks if they meet strict requirements with respect to specific power and thermal management. Highly conductive GDC-based electrolytes offer pathways to high power-density SOFCs at operating temperatures below 650ºC, but the rise in mixed ionic electronic conductivity (MIEC) above 650ºC reduces open circuit voltages and thus fuel cell efficiency [1,2]. This necessitates thermal management to maintain operating temperatures and mitigate thermo-mechanical stresses within an SOFC. Thin-film YSZ electrolytes offer lower power densities below 650ºC, but avoid the penalties associated with MIEC behavior at higher temperatures and therefore reduce the challenges associated with thermal management at high power densities. In this work, a model-based approach is used to compare SOFC stack operation with thin-film YSZ electrolytes and with GDC-based electrolytes for operation on hydrogen and reformate fuels at high-power densities relevant for transportation applications.To calibrate models to experimental cell performance, polarization curves of a commercially available YSZ-based cell operating between 600-750ºC and of a high-power-density GDC cell operating between 500-650ºC are used to fit electrochemical model parameters for both electrolytes. Modeling of the YSZ based cell can neglect electronic charge transfer through the membrane electrolyte, but GDC-cell modeling must account for the multiple charge carriers (ceria polarons and oxygen vacancies) in the electrolyte [3]. Electrochemical parameters for ionic conductivities and electrochemical reaction rate parameters for oxide cathodes and nickel-electrolyte-composite anodes are fit to the experimental polarization data over the broad range of operating temperatures. Global rate expressions to account for internal reforming on the active nickel surfaces of anode are adopted from literature [4,5]. The calibrated cell model for each cell type is adopted to a down-the-channel discretized cell simulation to predict heat loss and temperature gradients at high current densities.This presentation compares GDC- and YSZ-based SOFCs in high power-density applications from fundamental and practical perspectives. The open-circuit voltages for GDC-based cells drops with increasing temperature to about 0.85 V/cell at 650°C which is lower than the Nernst open-circuit voltage of YSZ-based cells (≥ 1.05 V/cell) at similar conditions. Both types of cells can sustain power densities around 1.0 W/cm2 with high excess cathode air ratios ≥ 5 to keep temperature gradients near 10°C/cm. These results show that GDC-based cells support higher power densities at lower cell flow inlet temperatures < 600°C, whereas thin-film YSZ cells provide superior performance at flow inlets that drive cell temperatures > 600°C. Higher stack power densities > 1.0 W/cm2 must be supported by stack designs that alleviate high thermal stresses and allow steeper gradients of temperature. A summary of stack design and operational strategies that meet the stringent requirements of high power-density operation will be presented in the light of the modeling resuls..

Construction of electrochemical model for high C-rate conditions in lithium-ion battery based on experimental analogy method

Lithium-ion batteries (LIBs) modeling is critical for the safe and efficient operation of electric vehicles (EVs) and energy storage systems (BESSs). Most electrochemical models are mainly suitable for normal temperature or low C-rate conditions (≤2 C). Meanwhile, the electrochemical model parameters are usually obtained by the half-cell testing method. This method has difficulty in disassembling batteries and obtaining model parameters quickly. To solve this problem, the internal electrochemical behavior of LIBs under high-C rate conditions is first studied in this paper. Through the above theoretical analysis, the relationship between the solid phase diffusion coefficient, the reaction rate constant and temperature/concentration must be considered under high C-rate conditions. Then a fast calibration method for electrochemical model parameters is proposed, and a variable parameter high C-rate model is established. Finally, the variable parameter high C-rate model is validated at different rates of 5 °C, 25 °C and 55 °C. The results show that the mean absolute errors (MAE) of the variable parameter high C-rate model are within 13 mV under low C-rate conditions. Under the high C-rate condition (≤6 C), the MAEs of the model are within 50 mV.

Parameter identification of lithium-ion battery pseudo-2-dimensional models using genetic algorithm and neural network cooperative optimization

The electrochemical model parameters of a lithium-ion battery are important indicators of its state-of-health, and many previous studies have proposed methods for identifying them. These identification methods must solve highly nonlinear optimization problems with many local optima. Hence, metaheuristic approaches are often employed. Most metaheuristics take a way to abandon worse solutions and make the most use of better solutions only. Such inefficient use of data leads to local optima problem in metaheuristics. To overcome these limitations, this paper proposes a novel parameter identification method in which a neural network cooperates with a genetic algorithm. The proposed method adopts an 1-dimensional convolutional neural network to learn the dynamics between the known input current and the corresponding simulated voltage. Although estimated parameters cause large output voltage errors, they are useful for building an electrochemical model and can be used to recommend highly probable parameter candidates. We clearly show through simulation and experiment that the electrochemical model parameters are identified more accurately and reliably compared with various existing results, owing to the high data efficiency of the proposed method.

Analytic Mapping between Porous Electrode Theory and Equivalent Circuit

Battery equivalent circuit models (ECMs) are frequently used in battery management systems of high end applications due to their low computational complexity, robustness and simplicity. Nevertheless, empirical nature of such models and lack of physiochemical background calls for excessive experimental parametrization of the ECMs to ensure their usability. Experimentally parameterized empirical models, in general, lack of prediction capability outside of the region of their parameterization. Due to these deficiencies of the ECMs, there is an increasing demand to develop the bridging methodology interlinking ECMs and continuum electrochemical models. Such a methodology introduces physiochemical significance to the ECMs by providing guidance to their topological structure and physiochemical meaning of their elements resultantly increasing their prediction capability and reducing the amount of data needed to parameterize the ECM.Constituent parts for the ECM with electrochemical basis already exist. Jamnik et.al [1] proposed the so called transmission lines (equivalent circuit representations) for several different electrochemical processes. Coupling constituent parts proposed by Jamnk et. al [1], one can design equivalent circuit model of the battery where every single element in ECM represent a distinctive part of the electrochemical system. With the goal to describe the electric impedance of the battery, several such models were proposed lately, i.e. [2, 3, 4]. Even though these models function well only for small harmonic perturbation (electric impedance simulation), their insightful results first clearly show that mapping between electrochemical battery model and equivalent circuit approach is possible and second they demonstrate the usefulness of electrochemically based ECMs. Nevertheless, none of the authors unambiguously shows the connection between physiochemical equations of the electrochemical model and the topology of the proposed circuit. Circuits are rather constructed based on intuition and justified by very plausible results that they generate. Here, we present the complete mapping between equivalent circuit model of one electrode and equations of porous electrode theory [5], which is one of the most commonly used continuum electrochemical model.The methodology that enables complete mapping between equations of porous electrode theory and equations of equivalent circuit follows finite volume discretization. The whole derivation is demonstrated for a one dimensional case but it can simply be generalized to higher dimensionality. First porous electrode was divided in finite number of control volumes along the thickness of the electrode. Selected number of control volumes determines the final resolution and computational complexity of the equivalent circuit. Four partial differential equations of porous electrode theory were discretized in the direction of electrode thickness by volume integration across all control volumes. Thereby, the system of partial differential equations is transformed to a large set of ordinary differential equations (ODE). Reformulation of the derived ODE system yields equations that can be interpreted as Kirchhoff’s laws of the electric circuit. Thereby identities between parameters of equivalent circuit and parameters of electrochemical model are established and thus complete mapping between both.Obtained general equivalent circuit model was first tested in the limit of small harmonic perturbation, since many already existing references reports the same case. The insightful results obtained by the model were compared to the analytical solution of the porous electrode theory equations for small harmonic perturbation calculated by Huang and Zhang [6]. Excellent matching between both shows credibility of the mapping that we propose. Further simulation was performed not only for the small harmonic perturbation but also for the high amplitude signals. Validity and plausibility of the proposed ECM is strengthened by the non-linear response of the proposed circuit to the high amplitude signals.

A new method for lithium-ion battery uniformity sorting based on internal criteria

Abstract Lithium-ion battery (LIB) uniformity has remarkable influence on the durability and safety of the battery pack. It is therefore important to assemble batteries with good consistency in a pack. This paper proposes a new LIB uniformity sorting method based on some internal criteria. Firstly, a simplified electrochemical model (EM) with parameter identification is introduced. Secondly, internal sorting criteria are selected from EM parameters according to their sensitivities and strength of correlation to aging. Thirdly, based on the proposed internal criteria and/or existing external criteria, four 4-series-connected LIB packs are assembled with cells being selected from 120 LiCoO2/graphite 14500 type LIB candidates and sorted by fuzzy C-means (FCM) algorithm A series of cyclic aging experiments are conducted and the results demonstrate that the proposed method can significantly prolong the cycle life of the pack and guarantee good voltage and state of charge (SOC) uniformity when internal criteria are used to sort cells for packs.

Electrochemical Model-Based Condition Monitoring via Experimentally Identified Li-Ion Battery Model and HPPC

Electrochemical model-based condition monitoring of a Li-Ion battery using an experimentally identified battery model and Hybrid Pulse Power Characterization (HPPC) cycle is presented in this paper. LiCoO2 cathode chemistry was chosen in this work due to its higher energy storage capabilities. Battery electrochemical model parameters are subject to change under severe or abusive operating conditions resulting in, for example, Navy over-discharged battery, 24 h over-discharged battery, and overcharged battery. Stated battery fault conditions can cause significant variations in a number of electrochemical battery model parameters from nominal values, and can be considered as separate models. Output error injection based partial differential algebraic equation (PDAE) observers have been used to generate the residual voltage signals in order to identify these abusive conditions. These residuals are then used in a Multiple Model Adaptive Estimation (MMAE) algorithm to detect the ongoing fault conditions of the battery. HPPC cycle simulated load profile based analysis shows that the proposed algorithm can detect and identify the stated fault conditions accurately using measured input current and terminal output voltage. The proposed model-based fault diagnosis can potentially improve the condition monitoring performance of a battery management system.

A transfer function type of simplified electrochemical model with modified boundary conditions and Padé approximation for Li-ion battery: Part 2. Modeling and parameter estimation

Abstract The electrochemistry-based battery model can provide physics-meaningful knowledge about the lithium-ion battery system with extensive computation burdens. To motivate the development of reduced order battery model, three major contributions have been made throughout this paper: (1) the transfer function type of simplified electrochemical model is proposed to address the current-voltage relationship with Pade approximation method and modified boundary conditions for electrolyte diffusion equations. The model performance has been verified under pulse charge/discharge and dynamic stress test (DST) profiles with the standard derivation less than 0.021 V and the runtime 50 times faster. (2) the parametric relationship between the equivalent circuit model and simplified electrochemical model has been established, which will enhance the comprehension level of two models with more in-depth physical significance and provide new methods for electrochemical model parameter estimation. (3) four simplified electrochemical model parameters: equivalent resistance R eq , effective diffusion coefficient in electrolyte phase D e eff , electrolyte phase volume fraction e and open circuit voltage (OCV), have been identified by the recursive least square (RLS) algorithm with the modified DST profiles under 45, 25 and 0 °C. The simulation results indicate that the proposed model coupled with RLS algorithm can achieve high accuracy for electrochemical parameter identification in dynamic scenarios.

Electrochemical model parameter identification of a lithium-ion battery using particle swarm optimization method

In this paper, a gradient-free optimization technique, namely particle swarm optimization (PSO) algorithm, is utilized to identify specific parameters of the electrochemical model of a Lithium-Ion battery with LiCoO2 cathode chemistry. Battery electrochemical model parameters are subject to change under severe or abusive operating conditions resulting in, for example, over-discharged battery, over-charged battery, etc. It is important for a battery management system to have these parameter changes fully captured in a bank of battery models that can be used to monitor battery conditions in real time. Here the PSO methodology has been successfully applied to identify four electrochemical model parameters that exhibit significant variations under severe operating conditions: solid phase diffusion coefficient at the positive electrode (cathode), solid phase diffusion coefficient at the negative electrode (anode), intercalation/de-intercalation reaction rate at the cathode, and intercalation/de-intercalation reaction rate at the anode. The identified model parameters were used to generate the respective battery models for both healthy and degraded batteries. These models were then validated by comparing the model output voltage with the experimental output voltage for the stated operating conditions. The identified Li-Ion battery electrochemical model parameters are within reasonable accuracy as evidenced by the experimental validation results.

Open-Circuit Voltage-Based State of Charge Estimation of Lithium-ion Battery Using Dual Neural Network Fusion Battery Model

ABSTRACT The OCV (open circuit voltage)-based method for SOC (state of charge) estimation by using the dual neural network fusion battery model is proposed in this paper. The weights of the constructed dual neural network fusion battery model can be used to describe the characteristics of the corresponding parameters of electrochemical model for the battery. The constructed dual neural network fusion battery model consists of two neural network models connected in series. The first part is a linear neural network battery model which can be used to identify parameters of the first-order electrochemical model or second-order electrochemical model for the battery, the second part is a BP (Back of Prorogation) neural network used for capturing the relationship between OCV and SOC. The DST (Dynamic Stress Test) data is adopted for training the dual neural network fusion battery model, by which the relationship between OCV and SOC is offline obtained. Under FUDS (Federal Urban Driving Schedule) condition, the experimental results show that the dual neural network fusion battery model can effectively estimate SOC based on the first-order electrochemical model or second-order electrochemical model.

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.

Reduced-Order Electrochemical Model Parameters Identification and State of Charge Estimation for Healthy and Aged Li-Ion Batteries—Part II: Aged Battery Model and State of Charge Estimation

Recently, extensive research has been conducted in the field of battery management systems due to increased interest in vehicles electrification. Parameters, such as battery state of charge (SOC) and state of health, are of critical importance to ensure safety, reliability, and prolong battery life. This paper includes the following contributions: 1) tracking reduced-order electrochemical battery model parameters variations as battery ages, using noninvasive genetic algorithm optimization technique; 2) the development of a battery aging model capable of capturing battery degradation by varying the effective electrode volume; and 3) estimation of the battery critical SOC using a new estimation strategy known as the smooth variable structure filter based on reduced-order electrochemical model. The proposed filter is used for SOC estimation and demonstrates strong robustness to modeling uncertainties, which is relatively high in case of reduced-order electrochemical models. Batteries used in this research are lithium-iron phosphate cells widely used in automotive applications. Extensive testing using real-world driving cycles is used for estimation strategy application and for conducting the aging test. Limitations of the proposed strategy are also highlighted.

Reduced-Order Electrochemical Model Parameters Identification and SOC Estimation for Healthy and Aged Li-Ion Batteries Part I: Parameterization Model Development for Healthy Batteries

The current phase in our transportation system represents a paradigm shift from conventional, fossil-fuel-based vehicles into the second-generation electric and hybrid vehicles. Electric vehicles (EVs) provide numerous advantages compared with conventional vehicles because they are more efficient, sustainable, greener, and cleaner. The commercial market penetration and success of EVs depend on the efficiency, safety, cost, and lifetime of the traction battery pack. One of the current key electrification challenges is to accurately estimate the battery pack state of charge (SOC) and state of health (SOH), and therefore provide an estimate of the remaining driving range at various battery states of life. To estimate the battery SOC, a high-fidelity battery model along with a robust, accurate estimation strategy is necessary. This paper provides three main contributions: 1) introducing a new SOC parameterization strategy and employing it in setting up optimizer constraints to estimate battery parameters; 2) identification of the full-set of the reduced-order electrochemical battery model parameters by using noninvasive genetic algorithm optimization on a fresh battery; and 3) model validation by using real-world driving cycles. Extensive tests have been conducted on lithium iron phosphate-based cells widely used in high-power automotive applications. Models can be effectively used onboard of battery management system.