Battery Degradation Model Research Articles

Nonlinear-Drifted Fractional Brownian Motion With Multiple Hidden State Variables for Remaining Useful Life Prediction of Lithium-Ion Batteries

Lithium-ion rechargeable batteries are widely used in various electronic products and equipment due to their immense benefits in power supplying. The exact remaining useful life (RUL) prediction of lithium-ion batteries has shown excellent achievements in preventing severe economic and security consequences incurred in failing to provide necessary power levels. Recently, the nonlinear-drifted fractional Brownian motion made quite a splash in RUL prediction, since its first hitting time distribution can be approximated by weak convergence theorem and time-space transformation. However, the previous RUL prediction methods based on fractional Brownian motion only considered current state measurement. In this paper, a prediction framework based on nonlinear-drifted fractional Brownian motion with multiple hidden state variables is put forward to estimate RUL. Specifically, all the parameters of nonlinear function are defined as specific hidden state variables of lithium-ion battery degradation model, and all the state measurements are used to posteriorly estimate the distribution of the multiple hidden state variables by unscented particle filter algorithm. Four sets of lithium-ion battery degradation data provided by NASA Ames Research Center are used to validate the proposed prediction framework. According to comparison study with other methods, the proposed prediction framework demonstrates greater precision in the RUL prediction.

Noninvasive Vehicle‐to‐Load Energy Management Strategy to Prevent Li‐Ion Batteries Premature Degradation

Today, electric vehicles available in the market aspire to offer different connections to the end user, for instance, Vehicle to Grid (V2G), Vehicle to Building (V2B), Vehicle to Home (V2H), Vehicle to Vehicle (V2V), and Vehicle to Load (V2L), among others. Notwithstanding these versatility options toward the development of a sustainable society, the additional degradation of the energy storage systems once those operate in extra discharge modes is inevitable. Therefore, in this paper, an energy management strategy (EMS) which operates autonomously and noninvasively as an additional layer to the battery management system (BMS) is proposed. The EMS limits the current flow avoiding high and low temperatures, low state of charge (SoC), high deep of discharge (DoD), noncentered DoD around an optimal SoC point, and high charge and discharge rates. The proposed EMS is evaluated by long‐term simulations with a Li‐Ion battery degradation model and realistic weather conditions, during standard driving cycles including the V2L operation. The effectiveness and simplicity of tuning of the proposed EMS allow estimating and increasing the life expectancy of the Li‐Ion battery bank, by limiting the energy used for V2L operation.

Charging Automation for Electric Vehicles: Is a Smaller Battery Good for the Wireless Charging Electric Vehicles?

Dynamic wireless charging (DWC) is an emerging technology that enables the batteries of electric vehicles (EVs) to charge automatically while the vehicles are in motion. The DWC-EV system addresses the challenges inherent in battery technology, such as the short driving range, long recharging time, and high price. Compared with conventional plug-in EVs, the DWC-EV can charge a battery more frequently because it can be done while the EV is in motion from the charging infrastructure installed on the road. In this paper, we analyze how this frequent-charging characteristic of DWC-EV can affect the battery lifetime in the DWC-EV. We first introduce a mathematical model to evaluate the economic cost of the DWC-EV for a given battery size. A battery degradation model is incorporated to account for the quantitative relationship between the installation of the charging infrastructure and battery life extension. We then use the model to analyze how the economic cost varies with the size of the battery. Our preliminary findings provide insight into the relationship between DWC from the charging infrastructure and the battery’s lifetime. Note to Practitioners —There is a tradeoff between power track allocation and battery size in DWC buses. It has been known that DWC buses need not equip a large battery because the battery can be charged frequently from the power track along the route. Also, it has been agreed that frequent shallow charging with DWC can improve the battery’s lifetime compared to infrequent deep charging. We verify these common beliefs and agreement with a mathematical approach with a widely used battery lifetime estimation model. Our quantitative model indicates that the DWC can positively improve battery lifetime, but this positive effect is always true only when the battery is large enough, even if the battery is charged frequently with DWC. The presented optimization model suggests that the lifelong economic benefit of DWC-based bus transit can be realized with optimal allocation of the power track with a sufficiently large battery.

Thermodynamics of Lead-Acid Battery Degradation: Application of the Degradation-Entropy Generation Methodology

This article details a lead-acid battery degradation model based on irreversible thermodynamics, which is then verified experimentally using commonly measured operational parameters. The model combines thermodynamic first principles with the Degradation-Entropy Generation theorem, to relate instantaneous and cyclic capacity fade (loss of useful charge-holding capacity) in the lead-acid battery to the entropy generated via the underlying dissipative physical processes responsible for battery degradation. Equations relating capacity fade to battery cycling are also formulated and verified. To show robustness of the approach, nonlinear data from uncontrolled and severely abusive battery cycling—including overdischarge—was measured and used to verify formulations. A near 100% agreement between the thermodynamic battery model and measurements is achieved. The model also gives rise to new material and design parameters to characterize all lead-acid batteries.

Optimization of compound power split configurations in PHEV bus for fuel consumption and battery degradation decreasing

Compound power-split configurations exhibit better fuel consumption than input and output power-split configurations. However, there is a need to understand how to design the best compound power-split configuration. In this paper, potential compound power-split configurations with two planetary gear sets are explored. Based on the planetary connection, there are 18 possible compound power-split configurations, but only 17 of those are applicable because of the lever length limitation. According to one-dimensional Equivalent Consumption Minimization Strategy and battery degradation model, the impact of compound power-split configuration design and control on fuel consumption and battery degradation are investigated. The results show the one-dimensional Equivalent Consumption Minimization Strategy based on Direct Transmit Points can further decrease the fuel consumption and battery degradation in compound power-split configurations. Similarly, the design parameters with lever length β close to −0.5 and lever length α close to 1.5 also lead to fuel consumption and battery degradation decreasing. The advantage of fuel consumption is observed because the system efficiency operation points are closer to the maximum efficiency line in optimized compound power-split design and control. Moreover, the compound power-split configuration can further decrease battery degradation in optimized design and control is because the current through the battery is less.

Battery aging in multi-energy microgrid design using mixed integer linear programming

This paper introduces a linear battery aging and degradation model to a multi-energy microgrid sizing model using mixed integer linear programming. The battery aging model and its integration into a larger microgrid sizing formulation are described. A case study is provided to explore the impact of considering battery aging on key results: optimal photovoltaic and storage capacities, optimal distributed energy resources operations strategies, and annual cost and generation metrics.The case study results suggest that considering battery degradation in optimal microgrid sizing problems significantly impacts the perceived value of storage. Depending on capacity loss and lifetime targets, considering battery degradation is shown to decrease optimal storage capacities between 6 and 92% versus scenarios that do not consider battery health. When imposing constant distributed energy resource capacities, inclusion of degradation can decrease optimal annual battery cycling by as much as a factor five and reduce total annual electricity cost savings from otherwise identical photovoltaic and storage systems by 5–12%. These results emphasize that as batteries grow in maturity and ubiquity for distributed energy applications, considering battery health and capacity loss is an essential component of any analytical tool or model to guide system planning and decision-making.

Battery degradation minimization oriented energy management strategy for plug-in hybrid electric bus with multi-energy storage system

The potential of reducing fuel consumption, harmful emission and cost benefit for plug-in electric hybrid buses depended largely on the power management strategy for specific hybrid electric powertrain configuration, especially for those with compound energy storage system. Hybrid energy storage system in this research comprise high energy lithium iron phosphate batteries and super-capacitors, therefore, the key of improving the life cycle cost-benefit is to extend the cycle life for lithium battery. This paper presents an optimal control strategy for the serial-parallel plug-in hybrid electric buses based on the lithium battery degradation model to minimize life cycle operating cost. To derive the globally optimal strategy, an algorithm based on two-dimensional Pontryagin's minimum principle is proposed. With the optimal strategy, the battery degradation is significantly reduced, and the total cost is reduced by 21.7% compared with a plug-in hybrid electric bus with single type energy storage. Further embodies the advantages of hybrid energy storage systems and optimization algorithms.

Deterministic models of Li-ion battery aging: It is a matter of scale

Abstract Due to the increasing interest on the Li-ion battery aging studies among researchers, there are numerous battery degradation models presented in literature. However, they are either focused on a single technology, form factor or scale. This can be challenging for researchers that typically have to bridge multiple technologies and are interested in crossing multiple scales, from material-level, to cell and module/pack level. This paper explores the models presented for Li-ion battery degradation in different scales from the material level to the application level. In each scale, the main aging variables are summarized, the mathematical presentation of models are analyzed and the merits and disadvantages of each scale is discussed. This review aims at bringing together methods and results for multiple technologies, form factors for the most common Li-ion battery technologies.

Characterization of the degradation process of lithium-ion batteries when discharged at different current rates

The use of energy storage devices, such as lithium-ion batteries, has become popular in many different domains and applications. Hence, it is relatively easy to find literature associated with problems of battery state-of-charge estimation and energy autonomy prognostics. Despite this fact, the characterization of battery degradation processes is still a matter of ongoing research. Indeed, most battery degradation models solely consider operation under nominal (or strictly controlled) conditions, although actual operating profiles (including discharge current) may differ significantly from those. In this context, this article proposes a lithium-ion battery degradation model that incorporates the impact of arbitrary discharge currents. Also, the proposed model, initially calibrated through data reported for a specific lithium-ion battery type, can characterize degradation curves for other lithium-ion batteries. Two case studies have been carried out to validate the proposed model, initially calibrated by using data from a Sony battery. The first case study uses our own experimental data obtained for a Panasonic lithium-ion cell, which was cycled and degraded at high current rates. The second case study considers the analysis of two public data sets available at the Prognostics Center of Excellence of NASA Ames Research Center website, for batteries cycled using nominal and 2-C (twice the nominal) discharge currents. Results show that the proposed model can characterize degradation processes properly, even when cycles are subject to different discharge currents and for batteries not manufactured by Sony (whose data were used for the initial calibration).

Optimal Operation of Energy Storage Systems Considering Forecasts and Battery Degradation

Energy storage systems have the potential to deliver value in multiple ways, and these must be traded off against one another. An operational strategy that aims to maximize the returned value of such a system can often be significantly improved with the use of forecasting—of demand, generation, and pricing—but consideration of battery degradation is important too. This paper proposes a stochastic dynamic programming approach to optimally operate an energy storage system across a receding horizon. The method operates an energy storage asset to deliver maximal lifetime value, by using available forecasts and by applying a multi-factor battery degradation model that takes into account operational impacts on system degradation. Applying the method to a dataset of a residential Australian customer base demonstrates that an optimally operated system returns a lifetime value which is 160% more, on average, than that of the same system operated using a set-point-based method applied in many settings today.

Hybrid Lithium Iron Phosphate Battery and Lithium Titanate Battery Systems for Electric Buses

Electric buses face problems of short driving range, slow charging, and high cost. To improve the performance of electric buses, a novel hybrid battery system (HBS) configuration consisting of lithium iron phosphate (LFP) batteries and Li-ion batteries with a Li4Ti5O12 (LTO) material anode is proposed. The configuration and control of the HBS are first studied, and a LFP battery degradation model is built. Simulation result indicates that the HBS can help us to mitigate LFP battery degradation. Then, the HBS is optimally sized for electric buses to achieve minimum cost. The daily bus operation and charging patterns as well as LFP battery degradation are considered. The optimal HBS has 10.7% and 19.3% lower total cost than the single LTO-battery and LFP-battery configurations, and has higher range flexibility than the single LTO-battery configuration.

A Statistical Approach for Modeling the Aging Effects in Li-Ion Energy Storage Systems

This paper presents a novel approach for the technical and economic assessment of Li-ion battery energy storage systems (BESS) in smart grids supported by renewable energy sources. The approach is based on the definition of a statistical battery degradation cost model (SBDCM), able to estimate the expected costs related to BESS aging, according to the statistical properties of its expected cycling patterns. This new approach can improve the assessment of the economical sustainability of BESSs in this kind of applications, helping in this way the planning processes in electricity infrastructures in presence of high penetration of intermittent renewable energy sources. The SBDCM proposed in this paper is a statistical generalization of a battery degradation model presented in the literature. The proposed approach has been validated numerically comparing the results with those of the deterministic model considering for the BESS a stochastic dataset of input signals. In order to test the usefulness of the proposed model in a real world application, the proposed SBDCM has been applied to the evaluation of the economic benefit associated to the development of distributed energy storage system scenarios in the Italian power system, aimed to provide ancillary services for supporting electricity market.

A study of the relationship between coulombic efficiency and capacity degradation of commercial lithium-ion batteries

High coulombic efficiency (CE) usually indicates a long battery cycle life. However, the relationship between long-term CE evolution and battery degradation is not fully understood yet. This paper explores the behavior of long-term CE and clarifies its relationship with capacity degradation. Cycle life tests are conducted on two types of mainstream commercial lithium-ion batteries. An incremental capacity (IC) analysis is then employed to identify battery aging mechanisms. Experimental observations along with in-depth discussions are presented regarding battery degradation, aging mechanisms, and CE evolution. From the experimental results, two typical degradation patterns are recognized. From the IC analysis, we observed that, in addition to a loss of lithium inventory, a loss of active material accelerates battery degradation and brings down CE values. From an electrochemical perspective, this paper establishes the relationship between CE evolution and capacity degradation. This relationship can help develop battery degradation models, estimate battery health states, and provide early failure warnings for a battery management system.

Applicability of available Li-ion battery degradation models for system and control algorithm design

Within electrified vehicle powertrains, lithium-ion battery performance degrades with aging and usage, resulting in a loss in both energy and power capacity. As a result, models used for system design and control algorithm development would ideally capture the impact of those efforts on battery capacity degradation, be computationally efficient, and simple enough to be used for algorithm development. This paper provides an assessment of the state-of-the-art in lithium-ion battery degradation models, including accuracy, computational complexity, and amenability to control algorithm development. Various aging and degradation models have been studied in the literature, including physics-based electrochemical models, semi-empirical models, and empirical models. Some of these models have been validated with experimental data; however, comparisons of pre-existing degradation models across multiple experimental data sets have not been previously published. Three representative models, a 1-d electrochemical model (a combination of performance model and degradation model), a semi-empirical degradation model (the performance is predicted by an equivalent circuit model) and an empirical degradation model (the performance is predicted by an equivalent circuit model), are compared against four published experimental data sets for a 2.3-Ah commercial graphite/LiFePO4 cell. Based on simulation results and comparisons to experimental data, the key differences in the aging factors captured by each of the models are summarized. The results show that the physics-based model is best able to capture results across all four representative data sets with an error less than 10%, but is 20x slower than the empirical model, and 134x slower than the semi-empirical model, making it unsuitable for powertrain system design and model-based algorithm development. Despite being computationally efficient, the semi-empirical and empirical models, when used under conditions that lie outside the calibration data set, exhibit up to 71% error in capacity loss prediction. Such models require expensive experimental data collection to recalibrate for every new application. Thus, in the author’s opinion, there exists a need for a physically-based model that generalizes well across operating conditions, is computationally efficient for model-based design, and simple enough for control algorithm development.

Optimal Placement and Sizing of Distributed Battery Storage in Low Voltage Grids Using Receding Horizon Control Strategies

In this paper we present a novel methodology for leveraging Receding Horizon Control (RHC), also known as Model Predictive Control (MPC) strategies for distributed battery storage in a planning problem using a Benders decomposition technique. Longer prediction horizons lead to better storage placement strategies but also higher computational complexity that can quickly become computationally prohibitive. The here proposed MPC strategy in conjunction with a Benders decomposition technique effectively reduces the computational complexity to a manageable level. We use the CIGRE low voltage (LV) benchmark grid as a case study for solving an optimal placement and sizing problem for different control strategies with different MPC prediction horizons. The objective of the MPC strategy is to maximize the photovoltaic (PV) utilization and minimize battery degradation in a local residential area, while satisfying all grid constraints. For this case study we show that the economic value of battery storage is higher when using MPC based storage control strategies than when using heuristic storage control strategies, because MPC strategies explicitly exploit the value of forecast information. The economic merit of this approach can be further increased by explicitly incorporating a battery degradation model in the MPC strategy.

Techno-economic analysis of the viability of residential photovoltaic systems using lithium-ion batteries for energy storage in the United Kingdom

Rooftop photovoltaic systems integrated with lithium-ion battery storage are a promising route for the decarbonisation of the UK’s power sector. From a consumer perspective, the financial benefits of lower utility costs and the potential of a financial return through providing grid services is a strong incentive to invest in PV-battery systems. Although battery storage is generally considered an effective means for reducing the energy mismatch between photovoltaic supply and building demand, it remains unclear when and under which conditions battery storage can be profitably operated within residential photovoltaic systems. This fact is particularly pertinent when battery degradation is considered within the decision framework. In this work, a commercially available coupled photovoltaic lithium-ion battery system is installed within a mid-sized UK family home. Photovoltaic energy generation and household electricity demand is recorded for more than one year. A comprehensive battery degradation model based on long-term ageing data collected from more than fifty long-term degradation experiments on commercial Lithium-ion batteries is developed. The comprehensive model accounts for all established modes of degradation including calendar ageing, capacity throughput, ambient temperature, state of charge, depth of discharge and current rate. The model is validated using cycling data and exhibited an average maximum transient error of 7.4% in capacity loss estimates and 7.3% in resistance rise estimates for over ayear of cycling. The battery ageing model is used to estimate the cost of battery degradation associated with cycling the battery according to the power profile logged from the residential property. A detailed cost-benefit analysis using the data collected from the property and the battery degradation model shows that, in terms of utility savings and export revenue, the integration of a battery yields no added benefit. This result was, in-part, attributed to the relatively basic control strategy and efficiency of the system. Furthermore, when the cost of battery degradation is included, the homeowner is subject to a significant financial loss.

On-Line Remaining Useful Life Prediction of Lithium-Ion Batteries Based on the Optimized Gray Model GM(1,1)

Lithium-ion battery on-line remaining useful life (RUL) prediction has become increasingly popular. The capacity and internal resistance are often used as the batteries’ health indicator (HI) for quantifying degradation and predicting the RUL. However, the capacity and internal resistance are too difficult to measure on-line due to the batteries’ internal state variables being inaccessible to sensors under operational conditions. In addition, measuring these variables requires accurate measurement devices, which can be expensive, and have limited applicability in practice. In this paper, a novel HI is extracted from the operating parameters of lithium-ion batteries for degradation models and RUL prediction. Moreover, the Box–Cox transformation is applied to improve the correlation between the extracted HI and the battery’s real capacity. Then, Pearson and Spearman correlation analyses are utilized to assess the similarity between the real capacity and the estimated capacity derived from the HI. An optimized gray model GM(1,1) is employed to predict the RUL based on the presented HI. The experimental results show that the proposed method is effective and accurate for battery degradation modeling and RUL prediction.

A Single Particle-Based Battery Degradation Model Including Chemical and Mechanical Degradation Physics

Accurate and rapid prediction of the status of a lithium-ion battery is an important process in Battery Management System (BMS). In this work, a single particle model is developed by focusing on crack propagation coupled with Solid Electrolyte Interface (SEI) layer formation and its evolution. The lithium ion loss due to the SEI layer evolution is integrated with our previously developed advanced single particle model that includes electrolytic physics. This model is fairly well predictive of capacity fade and voltage change as a function of cycle number and temperature. Despite its implementation in a single particle model, the results provide quantitative information on the role of SEI layer growth and crack propagation, and corresponding capacity fade and power loss.

Design-space exploration of series plug-in hybrid electric vehicles for medium-duty truck applications in a total cost-of-ownership framework

The light-duty vehicle market has seen some adoption of hybrid electric vehicles that is not reflected in the heavy-duty market. The major challenges associated with the heavy-duty segment are: (i) greater emphasis on economic viability, (ii) reluctance to take on risk associated with new technologies, and (iii) numerous diverse applications that preclude a one-size-fits-all approach to hybrid-electric powertrain design. To overcome these challenges, a model-based framework is required that enables the exploration and optimal design of powertrain architectures for diverse applications while capturing the impact of hybridization on the economics of ownership under different economic scenarios. This paper demonstrates such a framework that incorporates powertrain simulation and battery degradation models to predict fuel consumption, electrical energy consumption, and battery replacements. These results are combined with economic assumptions to enable the exploration of a large design space (which spans powertrain design & control variables, noise variables, and economic scenarios) from a total cost-of-ownership perspective to provide better insights to vehicle integrators, component manufacturers, and buyers of heavy-duty hybrid electric vehicles. The methodology is applied to series plug-in hybrid electric and extended-range electric powertrain architectures for medium duty truck applications. The results show that under the assumptions made, economically favorable solutions for series plug-in hybrid electric medium-duty trucks exist in the 2020 time-frame for the NY Composite Truck drive cycle, while for the HTUF Refuse Truck and HTUF Class 6 P&D Truck drive cycles, feasible solutions are not obtained until 2025 and 2030 time-frames respectively.

An On-Board Remaining Useful Life Estimation Algorithm for Lithium-Ion Batteries of Electric Vehicles

Battery remaining useful life (RUL) estimation is critical to battery management and performance optimization of electric vehicles (EVs). In this paper, we present an effective way to estimate RUL online by using the support vector machine (SVM) algorithm. By studying the characteristics of the battery degradation process, the rising of the terminal voltage and changing characteristics of the voltage derivative (DV) during the charging process are introduced as the training variables of the SVM algorithm to determine the battery RUL. The SVM is then applied to build the battery degradation model and predict the battery real cycle numbers. Experimental results prove that the built battery degradation model shows higher accuracy and less computation time compared with those of the neural network (NN) method, thereby making it a potential candidate for realizing online RUL estimation in a battery management system (BMS).