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Real-life batteries tend to experience a range of operating conditions, and undergo degradation due to a combination of both calendar and cycling aging. Onboard health estimation models typically use cycling aging data only, and account for at most one operating condition e.g., temperature, which can limit the accuracy of the models for state-of-health (SOH) estimation. In this paper, we utilize electrochemical impedance spectroscopy (EIS) data from 5 calendar-aged and 17 cycling-aged cells to perform SOH estimation under various operating conditions. The EIS curves are deconvoluted using the distribution of relaxation times (DRT) technique to map them onto a function $\textbf{g}$ which consists of distinct timescales representing different resistances inside the cell. These DRT curves, $\textbf{g}$, are then used as inputs to a long short-term memory (LSTM)-based neural network model for SOH estimation. We validate the model performance by testing it on ten different test sets, and achieve an average RMSPE of 1.69% across these sets., Comment: 6 pages, 7 figures

The increasing adoption of Lithium Iron Phosphate (LFP) batteries in Electric Vehicles is driven by their affordability, abundant material supply, and safety advantages. However, challenges arise in controlling/estimating unmeasurable LFP states such as state of charge (SOC), due to its flat open circuit voltage, hysteresis, and path dependence dynamics during intercalation and de-intercalation processes. The Core Shell Average Enhanced Single Particle Model (CSa-ESPM) effectively captures the electrochemical dynamics and phase transition behavior of LFP batteries by means of Partial Differential-Algebraic Equations (PDAEs). These governing PDAEs, including a moving boundary Ordinary Differential Equation (ODE), require a fine-grained spatial grid for accurate and stable solutions when employing the Finite Difference Method (FDM). This, in turn, leads to a computationally expensive system intractable for the design of real-time battery management system algorithms. In this study, we demonstrate that the Finite Volume Method (FVM) effectively discretizes the CSa-ESPM and provides accurate solutions with fewer than 4 control volumes while ensuring mass conservation across multi ple operational cycles. The resulting control-oriented reduced order FVM-based CSa-ESPM is experimentally validated using various C-rate load profiles and its observability is assessed through nonlinear observability analysis. Our results reveal that different current inputs and discrete equation numbers influence model observability, with non-observable regions identified where solid-phase concentration gradients are negligible., Comment: 6 pages, 4 figures

The single particle model (SPM) is a reduced electrochemical model that holds promise for applications in battery management systems due to its ability to accurately capture battery dynamics; however, the numerical discretization of the SPM requires careful consideration to ensure numerical stability and accuracy. In this paper, we present a comparative study of two mass-preserving numerical schemes for the SPM: the finite volume method and the control volume method. Using numerical simulations, we systematically evaluate the performance of these schemes, after independently calibrating the SPM discretized with each scheme to experimental data, and find a tradeoff between accuracy (quantified by voltage root-mean-square error) and computational time. Our findings provide insights into the selection of numerical schemes for the SPM, contributing to the advancement of battery modeling and simulation techniques., Comment: 6 pages, 4 figures

The electrification of heavy-duty commercial vehicles (HDCVs) is pivotal in reducing greenhouse gas emissions and urban air pollution; however, this transition poses significant challenges for the existing electric grid, which is not designed to meet the high electricity demands of HDCVs. This can lead to a less effective reduction in freight transportation's carbon intensity despite significant electrification efforts. Deploying renewable energy sources, such as photovoltaics, alongside energy storage solutions, is essential to address these challenges. This paper examines the current grid limitations and explores the critical role of microgrid deployment, integrating solar and battery energy storage systems, in supporting the electrification of HDCVs. We propose an integrated framework that is designed to enhance regional grid capacity and decrease carbon intensity by identifying viable sites where a microgrid can be deployed and provide estimates for the deployment cost. Furthermore, using this framework, we quantify the maximal impact of microgrid deployment in reducing CO2 emissions when we optimize the use of the available power. As a demonstration, we apply our framework to the region of the Port of Savannah, GA USA., Comment: 59 pages, 6 figures

Accurate estimation of battery state of health is crucial for effective electric vehicle battery management. Here, we propose five health indicators that can be extracted online from real-world electric vehicle operation and develop a machine learning-based method to estimate the battery state of health. The proposed indicators provide physical insights into the energy and power fade of the battery and enable accurate capacity estimation even with partially missing data. Moreover, they can be computed for portions of the charging profile and real-world driving discharging conditions, facilitating real-time battery degradation estimation. The indicators are computed using experimental data from five cells aged under electric vehicle conditions, and a linear regression model is used to estimate the state of health. The results show that models trained with power autocorrelation and energy-based features achieve capacity estimation with maximum absolute percentage error within 1.5% to 2.5% .

COBRAPRO is a new open-source physics-based battery modeling software with the capability to conduct closed-loop parameter optimization using experimental data. Physics-based battery models require systematic parameter calibration to accurately predict battery behavior across different usage scenarios. While parameter calibration is essential to predict the dynamic behavior of batteries, many existing open-source DFN modeling tools lack integrated parameter identification routines. COBRAPRO addresses this gap by featuring an embedded parameter optimization framework that optimizes the model parameters by minimizing the error between the simulated and experimentally observed current-voltage data. With COBRAPRO, users can non-invasively identify unknown battery model parameters for any given battery chemistry.

The reuse of retired electric vehicle batteries in grid energy storage offers environmental and economic benefits. This study concentrates on health monitoring algorithms for retired batteries deployed in grid storage. Over 15 months of testing, we collect, analyze, and publicize a dataset of second-life batteries, implementing a cycling protocol simulating grid energy storage load profiles within a 3-4 V voltage window. Four machine-learning-based health estimation models, relying on online-accessible features and initial capacity, are compared, with the selected model achieving a mean absolute percentage error below 2.3% on test data. Additionally, an adaptive online health estimation algorithm is proposed by integrating a clustering-based method, thus limiting estimation errors during online deployment. These results showcase the feasibility of repurposing retired batteries for second-life applications. Based on obtained data and power demand, these second-life batteries exhibit potential for over a decade of grid energy storage use., Comment: 16 pages, 8 figures

To enable the electrification of transportation systems, it is important to understand how technologies such as grid storage, solar photovoltaic systems, and control strategies can aid the deployment of electric vehicle charging at scale. In this work, we present EV-EcoSim, a co-simulation platform that couples electric vehicle charging, battery systems, solar photovoltaic systems, grid transformers, control strategies, and power distribution systems, to perform cost quantification and analyze the impacts of electric vehicle charging on the grid. This python-based platform can run a receding horizon control scheme for real-time operation and a one-shot control scheme for planning problems, with multi-timescale dynamics for different systems to simulate realistic scenarios. We demonstrate the utility of EV-EcoSim through a case study focused on economic evaluation of battery size to reduce electricity costs while considering impacts of fast charging on the power distribution grid. We present qualitative and quantitative evaluations on the battery size in tabulated results. The tabulated results delineate the trade-offs between candidate battery sizing solutions, providing comprehensive insights for decision-making under uncertainty. Additionally, we demonstrate the implications of the battery controller model fidelity on the system costs and show that the fidelity of the battery controller can completely change decisions made when planning an electric vehicle charging site., Comment: This paper has been accepted for publication at the IEEE Transactions on Smart Grid

A key challenge that is currently hindering the widespread use of retired electric vehicle (EV) batteries for second-life (SL) applications is the ability to accurately estimate and monitor their state of health (SOH). Second-life battery systems can be sourced from different battery packs with lack of knowledge of their historical usage. To tackle the in-the-field use of SL batteries, this paper introduces an online adaptive health estimation approach with guaranteed bounded-input-bounded-output (BIBO) stability. This method relies exclusively on operational data that can be accessed in real time from SL batteries. The effectiveness of the proposed approach is shown on a laboratory aged experimental data set of retired EV batteries. The estimator gains are dynamically adapted to accommodate the distinct characteristics of each individual cell, making it a promising candidate for future SL battery management systems (BMS2)., Comment: Update the paper within the 10-page limit

Lithium-ion batteries are playing a key role in the sustainable energy transition. To fully exploit the potential of this technology, a variety of modeling, estimation, and prediction problems need to be addressed to enhance its design and optimize its utilization. Batteries are complex electrochemical systems whose behavior drastically changes as a function of aging, temperature, C-rate, and state of charge, posing unique modeling and control research questions. In this tutorial paper, we provide insights into three battery modeling methodologies, namely first principle, machine learning, and hybrid modeling. Each approach has its own strengths and weaknesses, and by means of three case studies we describe main characteristics and challenges of each of the three methods.

In this paper, a core-shell enhanced single particle model for iron-phosphate battery cells is formulated, implemented, and verified. Starting from the description of the positive and negative electrodes charge and mass transport dynamics, the positive electrode intercalation and deintercalation phenomena and associated phase transitions are described with the core-shell modeling paradigm. Assuming two phases are formed in the positive electrode, one rich and one poor in lithium, a core-shrinking problem is formulated and the phase transition is modeled through a shell phase that covers the core one. A careful discretization of the coupled partial differential equations is proposed and used to convert the model into a system of ordinary differential equations. To ensure robust and accurate numerical solutions of the governing equations, a sensitivity analysis of numerical solutions is performed and the best setting, in terms of solver tolerances, solid phase concentration discretization points, and input current sampling time, is determined in a newly developed probabilistic framework. Finally, unknown model parameters are identified at different C-rate scenarios and the model is verified against experimental data.

Battery energy storage systems (BESSs) provide many benefits to the electricity grid, including stability, backup power, and flexibility in introducing more clean energy sources. As BESS penetration grows, knowledge of the uncertainty in the battery's state of charge (SOC) estimate is crucial for planning optimal BESS power injection trajectories. This paper proposes a framework for quantifying SOC estimation uncertainty based on battery rest periods. An uncertainty analysis is presented for a BESS participating in the frequency regulation market., Comment: To be published in the proceedings of MECC 2022

In this paper, a novel electrochemical model for LiFePO$_4$ battery cells that accounts for the positive particle lithium intercalation and deintercalation dynamics is proposed. Starting from the enhanced single particle model, mass transport and balance equations along with suitable boundary conditions are introduced to model the phase transformation phenomena during lithiation and delithiation in the positive electrode material. The lithium-poor and lithium-rich phases are modeled using the core-shell principle, where a core composition is encapsulated with a shell composition. The coupled partial differential equations describing the phase transformation are discretized using the finite difference method, from which a system of ordinary differential equations written in state-space representation is obtained. Finally, model parameter identification is performed using experimental data from a 49Ah LFP pouch cell.

This paper presents a combination of machine learning techniques to enable prompt evaluation of retired electric vehicle batteries as to either retain those batteries for a second-life application and extend their operation beyond the original and first intent or send them to recycle facilities. The proposed algorithm generates features from available battery current and voltage measurements with simple statistics, selects and ranks the features using correlation analysis, and employs Gaussian Process Regression enhanced with bagging. This approach is validated over publicly available aging datasets of more than 200 cells with slow and fast charging, with different cathode chemistries, and for diverse operating conditions. Promising results are observed based on multiple training-test partitions, wherein the mean of Root Mean Squared Percent Error and Mean Percent Error performance errors are found to be less than 1.48% and 1.29%, respectively, in the worst-case scenarios., Comment: 23 pages

This paper formulates and solves a multi-objective fast charging-minimum degradation optimal control problem (OCP) for a lithium-ion battery module made of series-connected cells equipped with an active balancing circuitry. The cells in the module are subject to heterogeneity induced by manufacturing defects and non-uniform operating conditions. Each cell is expressed via a coupled nonlinear electrochemical, thermal, and aging model and the direct collocation approach is employed to transcribe the OCP into a nonlinear programming problem (NLP). The proposed OCP is formulated under two different schemes of charging operation: (i) same-charging-time (OCP-SCT) and (ii) different-charging-time (OCP-DCT). The former assumes simultaneous charging of all cells irrespective of their initial conditions, whereas the latter allows for different charging times of the cells to account for heterogeneous initial conditions. The problem is solved for a module with two series-connected cells with intrinsic heterogeneity among them in terms of state of charge and state of health. Results show that the OCP-DCT scheme provides more flexibility to deal with heterogeneity, boasting of lower temperature increase, charging current amplitudes, and degradation. Finally, comparison with the common practice of constant current (CC) charging over a long-term cycling operation shows that promising savings, in terms of retained capacity, are attainable under both the control (OCP-SCT and OCP-DCT) schemes., Comment: 16 pages

In this work, we conduct a sensitivity analysis of the mean-value internal combustion engine exergy-based model, recently developed by the authors, with respect to different driving cycles, ambient temperatures, and exhaust gas recirculation rates. Such an analysis allows to assess how driving conditions and environment affect the exergetic behavior of the engine, providing insights on the system's inefficiency. Specifically, the work is carried out for a military series hybrid electric vehicle.

In this paper, a novel mean-value exergy-based modeling framework for internal combustion engines is developed. The characterization of combustion irreversibilities, thermal exchange between the in-cylinder mixture and the cylinder wall, and non-stoichiometric combustion allows for a comprehensive description of the availability transfer and destruction phenomena in the engine. The model is applicable to internal combustion engines operating both in steady-state and over a sequence of operating points and can be used to characterize the whole engine operating region, allowing to create static maps describing the exergetic behavior of the engine as a function of speed and load. The application of the proposed modeling strategy is shown for a turbocharged diesel engine. Ultimately, the static maps, while providing insightful information about inefficiencies over the whole operating field of the engine, are the enabling step for the development of exergy-based control strategies aiming at minimizing the overall operational losses of ground vehicles.

Exergy, or availability, is a thermodynamic concept representing the useful work that can be extracted from a system evolving from a given state to a reference state. It is also a system metric, formulated from the first and the second law of thermodynamics, encompassing the interactions between subsystems and the resulting entropy generation. In this paper, an exergy-based analysis for ground vehicles is proposed. The study, a first to the authors' knowledge, defines a comprehensive vehicle and powertrain-level modeling framework to quantify exergy transfer and destruction phenomena for the vehicle's longitudinal dynamics and its energy storage and conversion devices (namely, electrochemical energy storage, electric motor, and ICE). To show the capabilities of the proposed model in quantifying, locating, and ranking the sources of exergy losses, two case studies based on an electric vehicle and a parallel hybrid electric vehicle are analyzed considering a real-world driving cycle. This modeling framework can serve as a tool for the future development of ground vehicles management strategies aimed at minimizing exergy losses rather than fuel consumption.

This paper presents a novel battery modeling framework based on the enhanced single particle model (ESPM) to account for degradation mechanisms of second-life batteries. While accounting for the transport and electrochemical phenomena in the battery solid and electrolyte phases, the dominant anode-related aging mechanisms, namely, solid electrolyte interphase (SEI) layer growth and lithium plating, are modeled. For the first time, the loss of active material (LAM), which describes the tendency of anode and cathode, over time, to reduce the electrode material available for intercalation and deintercalation, is introduced in the ESPM. Moreover, the coupling of the aging modes with the LAM dynamics provides a comprehensive framework that can be employed for the prediction of both linear and non-linear capacity fade crucial to assess second-life battery. Thus, relying on data borrowed from [18], a model parameter identification and a comprehensive sensitivity analysis are performed to prove the effectiveness of the modeling approach., Comment: 8 pages, 5 figures

Battery aging is a natural process that contributes to capacity and power fade, resulting in a gradual performance degradation over time and usage. State of Charge (SOC) and State of Health (SOH) monitoring of an aging battery poses a challenging task to the Battery Management System (BMS) due to the lack of direct measurements. Estimation algorithms based on an electrochemical model that take into account the impact of aging on physical battery parameters can provide accurate information on lithium concentration and cell capacity over a battery's usable lifespan. A temperature-dependent electrochemical model, the Enhanced Single Particle Model (ESPM), forms the basis for the synthesis of an adaptive interconnected observer that exploits the relationship between capacity and power fade, due to the growth of Solid Electrolyte Interphase layer (SEI), to enable combined estimation of states (lithium concentration in both electrodes and cell capacity) and aging-sensitive transport parameters (anode diffusion coefficient and SEI layer ionic conductivity). The practical stability conditions for the adaptive observer are derived using Lyapunov's theory. Validation results against experimental data show a bounded capacity estimation error within 2% of its true value. Further, effectiveness of capacity estimation is tested for two cells at different stages of aging. Robustness of capacity estimates under measurement noise and sensor bias are studied., Comment: 16 pages