Electrochemical Model

In this work, a 1D polymer electrolyte membrane water electrolyzer (PEMWE) model that incorporates chemical degradation of the membrane is developed to study the influence of temperature and current density on the membrane degradation. In the 1D performance model, electronic and ionic transports through the different cell components are considered together with the electrochemical behavior of the anodic and cathodic catalyst layers. The membrane degradation model describes the oxygen cross-over from the anode to the cathode side, the formation of hydrogen peroxyde at the cathode side together with the subsequent formation of radicals via Fenton reactions involving metal-ion impurities and the membrane degradation. The development of the model is supported by specific single cell experiments to both validate the different modeling assumptions and determine some of the physical parameters involved in the performance and degradation models. The single-cell degradation tests confirm that most of the membrane degradation occurs at the cathode side and also show the strong influence of the temperature on the degradation rate. The effect of the current density on the degradation rate is more complex and presents a maximum at quite low current density. This phenomena, observed in the experiments, is well captured by the model. The model is then used to study the time evolution of the membrane thickness. The coupling between the performance and the chemical degradation models allows to capture the acceleration of membrane thinning.

Electric equivalent circuit (EEC) models have been widely used to interpret the inner dynamics of all type of batteries. Added to this, they also have been used to estimate state of charge (SOC) and state of health (SOH) values in combination with different methods. Four EEC models are considered for enhanced flooded lead acid batteries (EFB) which are widely used in micro hybrid vehicles. In this study, impedance and phase prediction capabilities of models throughout a frequency spectrum from 1 mHz to 10 kHz are compared with those of experimental results to investigate their consistency with the data. The battery is charged, discharged, and aged according to appropriate standards which imitates a lifetime of a micro hybrid vehicle battery under high current partial cycling. Impedance tests are repeated between different charge and health states until the end of the battery's lifetime. It is seen that adding transmission line elements to mimic the high porous electrode electrolyte interface to a double parallel constant phase element resistance model (ZARC) can increase the model data representing capability by 100%. The mean average percentage error (MAPE) of the conventional model with respect to data is 3.2% while the same value of the transmission line added model found as 1.6%. The results can be helpful to represent an EFB in complex simulation environments, which are used in automobile industry.

A numerical study with the aim of upgrading thermal performances of battery pack of electric vehicles is conducted for a full-size-scale battery pack with 22 modules (totally 5664 18650-type lithium-ion batteries contained) cooled by a channeled liquid flow. The heat generation of the battery is modeled based on experimental measurements. Experiments with one typical module (consisting of 180 batteries) of the pack, charging and discharging at different Crate (2C, 1C or 0.5C) at a specified liquid flow rate, are first carried out. The experimental results in what concerns maximum temperature in the battery module is in good agreement with the corresponding numerical predictions, demonstrating the reliability/fidelity and consequent accuracy of the developed model. The battery thermal management system is then finetuned to re-manage the flow distribution among modules for the sake of improving the thermal uniformity across the pack. The effect on the pack thermal performance of different charge/discharge Crates and flow rates are extensively investigated, and the results indicate that the pack is thermally wellperformed during 1C/0.5C discharge/charge operation with a fluid flow rate of 18 L/min; increasing the discharge/charge Crate worsens the battery pack's thermal characteristics and increasing the coolant flow rate makes the battery pack perform better.

With respect to channeled liquid cooling thermal management system of electric vehicle battery pack, a thermal model is established for a battery module consisting of 71 18650-type lithium-ion batteries. In this model, thermal-lumped treatment is implemented for each single battery in the module and heat generation of a single battery is determined based on experimental measurements. In particular, heat conduction between neighboring batteries and heat transfer from the battery to the fluid channel outer wall are carefully modeled. We study, by the developed model, the battery module's thermal behavior, and investigate the effects of discharge/charge Crate , the liquid flow rate, the heat exchange area between neighboring batteries, and the interfacing area of the battery and the channel outer wall. The simulation results corroborate the effectiveness of the cooling system. It is found from simulation results that: (1) increasing the discharge/charge Crate leads to higher temperature and worsens the temperature uniformity in the battery module; (2) increasing the liquid flow rate can significantly lower the temperature and improves the temperature uniformity in the battery module; (3) increasing the heat exchange area between neighboring batteries slightly improves the temperature uniformity in the battery module, but only has negligible effect on lowering the temperature of the module; (4) increasing the interfacing area of the battery and the channel outer wall can significantly lower the maximum temperature in the battery module but worsens the temperature uniformity in the module.

A numerical study with the aim of upgrading thermal performances of battery pack of electric vehicles is conducted for a full-size-scale battery pack with 22 modules (totally 5664 18650-type lithium-ion batteries contained) cooled by a channeled liquid flow. The heat generation of the battery is modeled based on experimental measurements. Experiments with one typical module (consisting of 180 batteries) of the pack, charging and discharging at different Crate (2C, 1C or 0.5C) at a specified liquid flow rate, are first carried out. The experimental results in what concerns maximum temperature in the battery module is in good agreement with the corresponding numerical predictions, demonstrating the reliability/fidelity and consequent accuracy of the developed model. The battery thermal management system is then finetuned to re-manage the flow distribution among modules for the sake of improving the thermal uniformity across the pack. The effect on the pack thermal performance of different charge/discharge Crates and flow rates are extensively investigated, and the results indicate that the pack is thermally wellperformed during 1C/0.5C discharge/charge operation with a fluid flow rate of 18 L/min; increasing the discharge/charge Crate worsens the battery pack's thermal characteristics and increasing the coolant flow rate makes the battery pack perform better.

With respect to channeled liquid cooling thermal management system of electric vehicle battery pack, a thermal model is established for a battery module consisting of 71 18650-type lithium-ion batteries. In this model, thermal-lumped treatment is implemented for each single battery in the module and heat generation of a single battery is determined based on experimental measurements. In particular, heat conduction between neighboring batteries and heat transfer from the battery to the fluid channel outer wall are carefully modeled. We study, by the developed model, the battery module's thermal behavior, and investigate the effects of discharge/charge Crate , the liquid flow rate, the heat exchange area between neighboring batteries, and the interfacing area of the battery and the channel outer wall. The simulation results corroborate the effectiveness of the cooling system. It is found from simulation results that: (1) increasing the discharge/charge Crate leads to higher temperature and worsens the temperature uniformity in the battery module; (2) increasing the liquid flow rate can significantly lower the temperature and improves the temperature uniformity in the battery module; (3) increasing the heat exchange area between neighboring batteries slightly improves the temperature uniformity in the battery module, but only has negligible effect on lowering the temperature of the module; (4) increasing the interfacing area of the battery and the channel outer wall can significantly lower the maximum temperature in the battery module but worsens the temperature uniformity in the module.

Based on proton conduction of polymeric electrolyte membrane (PEM) technology, the Polymer Electrolyte Membrane Water Electrolyser (PEMWE) offers an interesting solution for efficient hydrogen production. During the electrolysis of water in PEMWE, water is split into oxygen, protons and electrons at the anode and a water-gas two-phase flow results. The aim of this study is to investigate the link between the two-phase flow at the anode side and cell performance under low-pressure conditions. We have developed a two-dimensional stationary PEMWE model that takes into account electrochemical reaction, heat transfer, mass transfer (bubble flow) and charge balance through the Membrane Electrodes Assembly (MEA). In order to take into account the changing electrical behaviour, our model combines two scales of descriptions: at microscale within anodic active layer and MEA scale. The water management at both scales is strongly linked to the Not Coalesced Bubble regime (NCB regime) or the Coalesced Bubble regime (CB regime). Therefore, water content close to active surface areas depends on two-phase flow regimes. Our simulation results demonstrate that the coalesced phenomenon is associated with improvement of mass transfer, a decrease in ohmic resistance and an enhancement of the PEMWE efficiency. At low and medium current density values, the model has been validated using two separate experiment electrolysis cells.

Measurement and modeling of thermal performance in lithium-ion battery cell is crucial which directly affects the safety. Even though the operation of a lithium-ion battery cell is transient phenomena in most cases, most available thermal models for lithium-ion battery cell predicts only steady-state temperature fields. This paper presents a mathematical model to predict the transient temperature distributions of a large sized 20Ah-LiFePO4 prismatic battery at different Crates. For this, the Lithium-ion battery was placed in a vertical position on a stand inside the lab with an ambient air cooling and the battery is discharged under constant current rate of 1C, 2C, 3C, and 4C in order to provide quantitative data regarding thermal behaviour of lithium-ion batteries. Additionally, IR images are taken for the same battery cell during discharging. Model predictions are in good agreement with experimental data and also with an IR imaging for temperature profiles. The present results show that increased Crates results in increased temperature on the principle surface of the battery.

This paper proposes a new fast charging strategy for lithium-ion (Li-ion) batteries. The approach relies on an experimentally validated high-fidelity model describing battery electrochemical and thermal dynamics that determine the fast charging capability. Such a high-dimensional nonlinear dynamic model can be intractable to compute in real-time if it is fused with the extended Kalman filter or the unscented Kalman filter that is commonly used in the community of battery management. To significantly save computational efforts and achieve rapid convergence, the ensemble transform Kalman filter (ETKF) is selected and tailored to estimate the nonuniform Li-ion battery states. Then, a health-and safety-aware charging protocol is proposed based on successively applied proportional-integral (PI) control actions. The controller regulates charging rates using online battery state information and the imposed constraints, in which each PI control action automatically comes into play when its corresponding constraint is triggered. The proposed physical constraint-triggered PI charging control strategy with the ETKF is evaluated and compared with several prevalent alternatives. It shows that the derived controller can achieve close to the optimal solution in terms of charging time and trajectory, as determined by a nonlinear model predictive controller, but at a drastically reduced computational cost. Index Terms-Electrochemical model, ensemble transform Kalman filter (ETKF), fast charging, lithium plating, lithiumion (Li-ion) battery. NOMENCLATURE Symbol: C T Battery thermal capacitance (J/K). H Prediction horizon of model predictive control. I I Current due to molar flux of intercalation (A). I app Applied charging current (A). K P , K I Proportional and integral gains. M Order of the submodel for solid-phase diffusion. N j Number of control volumes of a domain. j ∈ {pos, sep, neg}.

The proton exchange membrane (PEMFC) fuel cell represents the energy of the future, in parallel with hydrogen. However, this technology must meet many technical challenges related to performance and durability before being sold on a large scale. It is well known that these challenges are closely linked to water management. This paper develops and implements a model of PEM fuel for simulation to make prediction on the water content. The proposed model includes a voltage evolution model based on the electrochemical and dynamics gases aspect, a water activity model to approximate relative humidity and a fuel cell spectroscopy impedance model to estimate the water content in order to make an accurate diagnosis. Furthermore, this work adopts a methods of modeling that presents a new solution to bring water into the fuel cell membrane, where it humidifies the Input gases (air and hydrogen) to a relative humidity over 0%. However, this solution causes a problem of flooding the membrane in the PEMFC. In this work, an Electrochemical Impedance Spectroscopy (EIS) is used to make the flooding and drying diagnosis in the fuel cell.  The strengths of this proposed model are that it can be used at the same time in the field of power systems and for water diagnosis. This model predicts the response of step change in the load demand, and the water rate introduced by air into the fuel cell. The simulation results are presented with a qualitative interpretation of PEM fuel cell flooding and drying behavior.

In this paper, multiple-model adaptive estimation techniques have been successfully applied to fault detection and identification in lithium-ion batteries. The diagnostic performance of a battery depends greatly on the modeling technique used in representing the system and the associated faults under investigation. Here, both linear and non-linear battery modeling techniques are evaluated and the effects of battery model and noise estimation on the overcharge and over-discharge fault diagnosis performance are studied. Based on the experimental data obtained under the same fault scenarios for a single cell, the non-linear model based detection method is found to perform much better in accurately detecting the faults in real time when compared to those using linear model based method.

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. LiCoO 2 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.

In this paper, multiple-model adaptive estimation techniques have been successfully applied to fault detection and identification in lithium-ion batteries. The diagnostic performance of a battery depends greatly on the modeling technique used in representing the system and the associated faults under investigation. Here, both linear and non-linear battery modeling techniques are evaluated and the effects of battery model and noise estimation on the overcharge and over-discharge fault diagnosis performance are studied. Based on the experimental data obtained under the same fault scenarios for a single cell, the non-linear model based detection method is found to perform much better in accurately detecting the faults in real time when compared to those using linear model based method.

An electrochemical model is presented to calculate the rebar shape time-evolution in reinforced mortar specimens during forced corrosion tests. This provides a more realistic description than the usually used geometric models. The current distribution along the rebar perimeter is calculated by using Finite Element Method (FEM) to solve Laplace equation. Then, Faraday’s law is used to relate current distribution to rebar volume increase due to corrosion products creation. The shape of the rebar section is obtained as a function of corrosion time.

Obtaining tools to analyze and predict the performance of batteries is a non-trivial challenge because it involves non-destructive evaluation procedures. At the research level, the development of sensors to allow cell-level monitoring is an innovative path, and electrochemical impedance spectrometry (EIS) has been identified as one of the most promising tools, as is the generation of advanced multivariable models that integrate environmental and internal-battery information. In this article, we describe an algorithm that automatically identifies a battery-equivalent electrochemical model based on electroscopic impedance data. This algorithm allows in operando monitoring of variations in the equivalent circuit parameters that will be used to further estimate variations in the state of health (SoH) and state of charge (SoC) of the battery based on a correlation with experimental aging data corresponding to states of failure or degradation. In the current work, the authors propose a tw...

Obtaining tools to analyze and predict the performance of batteries is a non-trivial challenge because it involves non-destructive evaluation procedures. At the research level, the development of sensors to allow cell-level monitoring is an innovative path, and electrochemical impedance spectrometry (EIS) has been identified as one of the most promising tools, as is the generation of advanced multivariable models that integrate environmental and internal-battery information. In this article, we describe an algorithm that automatically identifies a battery-equivalent electrochemical model based on electroscopic impedance data. This algorithm allows in operando monitoring of variations in the equivalent circuit parameters that will be used to further estimate variations in the state of health (SoH) and state of charge (SoC) of the battery based on a correlation with experimental aging data corresponding to states of failure or degradation. In the current work, the authors propose a tw...

An improved electrochemical model is developed to study the ammonia fed solid oxide fuel cell based on proton conducting electrolyte (SOFC-H). Including the chemical reaction kinetics of NH 3 catalytic thermal decomposition, the present model can be used to predict the performance of the NH 3 fed SOFC-H at an intermediate temperature (i.e. 773 K). Comparison between the simulation results using the present model and experimental data from literature validates the accuracy of this model. Parametrical analyses reveal that at a high operating temperature (i.e. 1073 K), the NH 3 fuel is completely decomposed to H 2 and N 2 within a very thin layer (30 m) near the anode surface of an SOFC-H. It is also found that operating the NH 3 fed SOFC-H at an intermediate temperature of 773 K is feasible due to sufficiently high rate of NH 3 decomposition. However, further decreasing the temperature to 673 K is not recommended as less than 10% NH 3 fuel can be decomposed to H 2 and N 2 in the SOFC-H. The effects of current density and electrode microstructure on the performance of the NH 3 fed SOFC-H are also studied. It is found that increasing electrode porosity and pore size is beneficial to increase the partial pressure of H 2 at the anode-electrolyte interface. The model developed in this paper can be extended to 2D or 3D models to study practical tubular or planar SOFCs.

Electrochemical gating at the single molecule level of viologen molecular bridges in ionic liquids is examined. Contrary to previous data recorded in aqueous electrolytes, a clear and sharp peak in the single molecule conductance versus electrochemical potential data is obtained in ionic liquids. These data are rationalized in terms of a two-step electrochemical model for charge transport across the redox bridge. In this model the gate coupling in the ionic liquid is found to be fully effective with a modeled gate coupling parameter, ξ, of unity. This compares to a much lower gate coupling parameter of 0.2 for the equivalent aqueous gating system. This study shows that ionic liquids are far more effective media for gating the conductance of single molecules than either solid-state three-terminal platforms created using nanolithography, or aqueous media.

An electrochemical model is presented to calculate the rebar shape time-evolution in reinforced mortar specimens during forced corrosion tests. This provides a more realistic description than the usually used geometric models. The current distribution along the rebar perimeter is calculated by using Finite Element Method (FEM) to solve Laplace equation. Then, Faraday’s law is used to relate current distribution to rebar volume increase due to corrosion products creation. The shape of the rebar section is obtained as a function of corrosion time.

In this paper, we propose a solution for the control of the state-of-charge of a lithium-ion (Li-ion) battery cell. The aim is to design a control scheme able to charge the battery in a fast way while ensuring that the safety constraints of the electrochemical model (ECheM) of the battery are not violated. The proposed solution is based on a novel computationally efficient formulation of the Reference Governor (RG) able to deal with the union of linear constraints and which has been designed on the basis of a reduced ECheM, namely the equivalent-hydraulic model (EHM). Using suitable safety margins, the satisfaction of the constraints on the EHM ensures the satisfaction of the constraints on the full-order ECheM. Simulation results obtained on an accurate simulator show that the proposed method, if compared with classical charge strategies, is able to considerably improve the charge performance while ensuring the satisfaction of the constraints. These findings are validated experimentally on a Li-ion graphite/LCO battery.

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. LiCoO 2 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.

The fast charge battery control problem is characterized by the need to have a sufficiently detailed model that can capture both the charging process and the inevitable constraints that limit the rate of charging due to battery state of health requirements. Presently, it appears the minimal modeling requirements to address the charging problem in model based fashion are unknown. This work seeks to develop a modeling methodology covering a large range of applications through systematically simplifying the partial differential equations that describe battery dynamics. The effects of grid resolution and polynomial order on the complexity and accuracy of reduced order models have been investigated to provide insight into the minimum modeling requirements at different charge rates. The proposed models are intended for controller design and optimization applications including fast charge control.

This paper presents a review of studies on mathematical modeling of solid oxide fuel cells (SOFCs) with respect to the tubular and planar configurations. In this work, both configurations are divided into five subsystems and the factors such as mass/energy/momentum transfer, diffusion through porous media, electrochemical reactions with and without CO oxidation, shift and reforming reactions, and polarization losses inside the subsystems are discussed. Using variety of fuels fed to SOFCs is issued and their effect on the system is compared briefly. A short review of solid oxide fuel cell configurations and different flow manifolding are also presented in this study. Novel models based on statistical data-driven approach existing in the literatures are considered shortly. Although many studies on solid oxide fuel cells modeling have been done, still more research needs to be done to improve the models in order to predict the fuel cell behaviors more accurately. At the end of this pap...