Battery Life Model Research Articles

Mathematical model of a battery energy storage for a standalone solar photovoltaic plant

Relevance. One of the priority areas for modern energy development is the active use of renewable energy technologies, the leading position among which in terms of the volume of commissioned generating capacity and areas of practical application is occupied by photovoltaics. In recent years, solar photovoltaic plants are increasingly being used as part of autonomous power supply systems, which is largely facilitated by a significant reduction in the cost of their components due to improved technology. Autonomous power supply systems can vary significantly in power, operating conditions, requirements for uninterrupted power supply and many other factors. This determines the high importance of the task of choosing the composition of the main electrical equipment that ensures optimal technical and economic indicators of the designed energy system. To make a reasonable choice of the equipment of an autonomous photovoltaic power plant, simulation models of all its main components are required that adequately reflect their performance characteristics under real operating conditions. An important component of autonomous photovoltaic plants is the energy storage device, which includes a battery and a solar controller that manages the energy balance of the power plant. The settings of the solar controller largely determine the operating modes of the photovoltaic power plant, on which the service life of the batteries primarily depends. Taking into account the fact that the costs of energy storage constitute a significant share of the costs of the total financial investments in the designed power plant, the problem of reliably assessing the service life of batteries is very relevant. Aim. Development of a mathematical model of energy storage system for the design and optimization of the equipment of autonomous photovoltaic plants. Methods. Mathematical and numerical modeling using the MatLab/Simulink software package. Results. A mathematical model of a battery has been developed, based on the modified Shepherd model and the kinetic model of a rechargeable battery. The model is universal and can be used to simulate the static and dynamic characteristics of different types of batteries. To identify model parameters, only the technical specification data provided by the manufacturer is sufficient. The complex model includes a battery life model, which allows you to dynamically adjust the available maximum battery capacity during operation.

Hybrid energy storage system for electric motorcycles: Technical and economic analysis

This paper presents the multiple energy storage system usability for electric motorcycle focused on hybrid topology. This study focuses on evaluating the cost-effectiveness of a hybrid energy storage system (HESS) for e-motorcycles over a 10-year period by considering the number of battery replacements instead of solely the initial system price. The motorcycle studied in this manuscript, is a recreational electric motorcycle utilized as an experimental test bench in EV-SCHS laboratory at the OJEN company. The 10-year equivalent price of the energy storage system includes both the initial purchase cost and the cost of battery replacements over the system's lifespan. A battery life model is essential for estimating the frequency of replacements over the 10-year period. Incorporating ultracapacitors (UC) in the HESS enhances power specifications, leading to improved acceleration and regenerative braking capabilities. This reduces battery current and extends battery life, resulting in fewer required replacements and lower overall system costs over the 10-year period. The study findings demonstrate that optimally-sized HESS configurations offer favorable power specifications, with the 10-year equivalent price of HESS being $3466 lower than that of conventional energy storage systems, despite the initial price of HESS being $833 higher.

Online battery aging calculation in plug-in hybrid electric vehicle considering driving condition

ABSTRACT Online calculation of battery capacity loss and its instantaneous remaining life for electric and hybrid electric vehicles is a challenging subject, particularly for designing and optimizing vehicle energy management in real-life driving conditions. This paper presents an online method for estimating plug-in hybrid electric vehicle battery degradation, considering the driving conditions. For this purpose, a national parallel plug-in hybrid electric vehicle is employed, where its components have been sized based on some experimental map characteristics using a genetic algorithm. Also, a real-world driving cycle is developed based on the data gathered in the actual traffic conditions in Tehran. The vehicle’s energy management system is designed using an adaptive equivalent consumption minimization strategy. In addition, an empirical battery life model combined with an online cycle counting method is used for battery aging calculation. To evaluate the effectiveness of the proposed approach, the capacity fade of the vehicle battery over various driving cycles has been calculated. The comparison of the results confirms the efficacy of the proposed algorithm compared to the Rainflow counting algorithm. Applying the Rainflow to all driving cycles yields consistent outcomes. However, when employing the suggested method, capacity losses of approximately 2.4%, 1.9%, 2.1%, and 1.4% are detected in Tehran, FTP-75, WLTP, and NEDC, respectively, following one hundred driving cycles. This means the capacity loss increases by 35%, 50%, and 71% for FTP-75, WLTP, and Tehran, respectively, compared with the NEDC driving cycle.

Research on the interaction between energy consumption and power battery life during electric vehicle acceleration

Most studies on the acceleration process of electric vehicle focus on reducing energy consumption, but do not consider the impact of the power battery discharge current and its change rate on the battery life. Therefore, this paper studied the interaction between electric vehicle energy consumption and power battery capacity attenuation during acceleration. First, a power battery life model for electric vehicle under driving conditions is established, and the percentage of battery capacity loss per kilometer is used to measure the capacity loss under different acceleration conditions. Then, the relationship between the percentage of battery capacity loss per kilometer and velocity and acceleration is explored, and the capacity attenuation mechanism of power battery under different acceleration processes is analyzed. Finally, the energy consumption and battery capacity attenuation is studied when the electric vehicle accelerated with multiple accelerations curves, and the interaction of the first acceleration and acceleration time on the electric vehicle energy consumption and the power battery capacity attenuation characteristics is discussed. The research results indicate that when the electric vehicle accelerates with different multiple accelerations curves, the change of energy consumption per kilometer and percentage of battery capacity loss per kilometer with acceleration and acceleration time is different, and the change of the two is basically opposite.

Hybrid energy storage system control and capacity allocation considering battery state of charge self-recovery and capacity attenuation in wind farm

Hybrid energy storage system (HESS) can cope with the complexity of wind power. But frequent charging and discharging will accelerate its life loss, and affect the long-term wind power smoothing effect and economy of HESS. Firstly, for the operational control of HESS, a bi-objective model predictive control (MPC) -weighted moving average (WMA) strategy for energy storage target power controlling is proposed, considering both energy storage state of charge (SOC) self-recovery and grid-connected power stabilization. The strategy can quickly adjust the SOC of HESS in the wind power smoothing process and reduce the battery's life loss. Then, since the energy storage capacity determines its power smoothing ability, this paper proposes a battery life model considering the effective capacity attenuation caused by calendar aging, and introduces it into the HESS cost calculation model to optimize the capacity allocation. Finally, combined with the wind power data, the simulation verifies that the proposed strategy can effectively balance the contradiction between energy storage lifetime and wind power smoothing effect. Simultaneously, the HESS optimized capacity allocation results considering battery's effective capacity attenuation can ensure the long-term wind power smoothing effect and better HESS operational states, contributing to the long-term and stable operation of wind-storage combined system.

Optimization of Energy Storage System Economics and Controls by Incorporating Battery Degradation Costs in REopt®

The use of stationary electrochemical energy storage systems utilizing lithium-ion batteries has increased rapidly as the production scale has grown and price for lithium-ion batteries has decreased. These energy storage systems are crucial for maintaining grid resiliency, especially for grids operating with high penetration of renewable energy generation assets or with a variety of distributed energy generation and storage systems. One challenging factor for the adoption of battery energy storage systems is estimating the proper sizing, in terms of both power and energy, that minimizes total cost; properly sizing energy storage systems is difficult in simple cases, where a battery is costed independently of any other systems, but is extremely challenging when building loads and electrical generation by photovoltaic resources are also considered. REopt® is a techoeconomic optimization tool developed by NREL to address these challenges. Previously, battery degradation has been priced by simply assuming a 10-year replacement schedule for battery systems. However, this does not account for varying degradation trends observed across real-world batteries, or inform degradation-aware control strategies to optimize battery dispatch and extend lifetime.This work incorporates a battery life model into REopt. The battery life model is linearized so that it may be solvable within the constrains of a mixed-integer linear optimization problem. To achieve the best possible accuracy for lifetime estimates given these constraints, parameters for the battery life model in REopt are estimated by fitting 20-year simulations of battery life after identifying a state-space battery degradation model from accelerated aging data. Comparisons of battery life predicted in REopt and from the state-space battery degradation model are made to ensure validity of lifetime estimates made by REopt.Battery life impacts system cost through three decision variables: battery sizing, daily state-of-charge, and daily energy-throughput. The cost of battery degradation as a function of these control variables is then estimated assuming two possible maintenance strategies: replacement, where the entire battery system is replaced if cells reach an end-of-life capacity threshold; and augmentation, which establishes a fund to pay for continual purchase of new batteries to maintain the initial energy capacity of the system. These two strategies offer conservative (for replacement) and optimistic (for augmentation) bounds for total system cost. The degradation cost incurred by these strategies is then used to inform battery dispatch decisions, operating the battery in a degradation-aware manner that maximizes battery lifetime while also providing energy when economically favorable. Because the mixed-integer linear program has perfect foresight of future energy needs, batteries are often operated using ‘just-in-time’ charging, which is unrealistic, as no energy is left in the storage system to perform other energy services or to serve as emergency back-up power. To combat this, an inequality constraint on the average annual state-of-charge is imposed, and the sensitivity of system cost to average stored energy, e.g., the cost of system resiliency, can be quantified. Analysis of results has several conclusions, for instance, increasing battery capacity to provide more flexibility for dispatch, enabling the extension of useful life beyond 10 years and resulting in greater avoided utility costs per unit for energy storage while providing more energy storage for grid resiliency.

Experimental investigation on the characteristics of coulombic efficiency of lithium-ion batteries considering different influencing factors

Coulombic efficiency (CE) can quantitatively reflect the side reactions inside the battery and a long battery cycle life. This study proposes a novel quantitative method for characterizing the side reactions of lithium-ion batteries. The main measuring principle is the open circuit state of the battery is simulated through long-term constant-voltage charging, and an ultra-high precision charger measures the average current to quantify the side effects of the battery. The relationship among battery side reaction current, state-of-charge (SOC), and temperature is accurately measured and investigated in detail. Then, the battery CE is determined under different ageing degrees, temperatures, and SOCs. In particular, the evolution process of battery CE in the low SOC range is discussed. Finally, a battery life model related to CE is proposed and verified. The experimental results show that the proposed model has satisfactory accuracy and does not require a large number of test data, which has the application potential to predict the full-lifespan life of new batteries. The study is valuable for understanding and evaluating the complex side effects in the battery ageing process and also provides a new idea for the ageing prediction of new batteries.

Energy arbitrage optimization of lithium-ion battery considering short-term revenue and long-term battery life loss

To achieve the ambitious goal of net-zero by 2050, the power sector in many countries has been increasingly using renewable energy sources (RES). The power system balance will be significantly challenged due to the intermittency of RES. Lithium-ion battery energy storage systems (BESS) can effectively address the challenge by providing flexibility to fill the mismatch between the intermittent supply and the varying demand, generating revenues for BESS to payback the initial investment. However, every grid participation also results in an inevitable lifetime loss. From the asset owner’s perspective, therefore, it is important to balance the short-term revenue from the fluctuating electrical market with the long-term battery life loss. To achieve this in this study, first, a novel online-applied battery life model is established, which is computationally efficient to comprehensively consider the battery’s historical aging, state of charge (SOC), charge–discharge rate (Crate). Then, an online-applied sliding-window dynamic programming (SWDP) strategy is proposed to optimize short-term grid service revenues and long-term battery life losses. The SWDP is also compared with an offline-applied dynamic programming (DP) strategy. The simulation results show that the cost due to battery life decay is significant, which indicates the importance of tracking the battery life loss in the battery asset management. Additionally, the prediction accuracy of electricity price significantly influences the performance of SWDP strategy. The BESS’s total profit can reduce by half in the considered case study if the electricity prediction error is 12.5%.

Improvement of PHEV Equivalent Fuel Economy and Battery Life by Applying Traffic-Based SOC Management

Improvement of plug-in hybrid electric vehicle (PHEV) equivalent fuel consumption (EFC) and battery life are significant issues in the design of PHEVs. This research aims to develop an adaptive traffic-based controller to improve fuel economy and battery life. The optimal state of charge (SOC) trajectories in real-world and standard cycles are extracted using the modified dynamic programming (MDP) approach. The optimal data is clustered based on the driving features, under the light of fuzzy clustering. Then, a control map is formed based on the clustered data to estimate SOC trajectories as a reference in an adaptive control strategy. A battery life model is employed to investigate the effect of the proposed method on battery aging. This study reveals that traffic-based SOC management simultaneously reduces the operating and maintenance costs since it improves the equivalent fuel economy and battery life in various driving cycles. Moreover, the suggested energy management strategy is implemented on an embedded system by applying the model-based design (MBD) method. The comparison of hardware-in-the-loop (HIL) and model-in-the-loop (MIL) simulation shows that the suggested strategy is implementable and effective for real applications.

Lithium-Ion Battery Life Model with Electrode Cracking and Early-Life Break-in Processes

This paper develops a physically justified reduced-order capacity fade model from accelerated calendar- and cycle-aging data for 32 lithium-ion (Li-ion) graphite/nickel-manganese-cobalt (NMC) cells. The large data set reveals temperature-, charge C-rate-, depth-of-discharge-, and state of charge (SOC)-dependent degradation patterns that would be unobserved in a smaller test matrix. Model structure is informed by incremental capacity analysis that shows loss of lithium inventory and cathode-material loss as the dominant capacity fade mechanisms. The model includes terms attributable to solid-electrolyte interface (SEI) growth, electrode cracking, cycling-driven acceleration of SEI growth, and “break-in” mechanisms that slightly decrease or increase available Li inventory early in life. The study explores what mathematical couplings of these mechanisms best describe calendar aging, cycle aging, and mixed calendar/cycle aging. Various approaches are discussed for extracting relevant stress factors from complex cycling profiles to predict lifetime during real-world battery loads using models trained on constant-current laboratory test results. The complexity of the present human-driven model identification process motivates future work in machine learning to more widely search and statistically discern the optimal model that correctly extrapolates capacity fade based on physical knowledge.

Improvement of Battery Life and Energy Economy for Electric Vehicles with Two-Speed Transmission

With the current energy environment background and development of the electrification of the automotive industry, a comprehensive economic indicator, in which the battery aging is further considered on the basis of conventional energy consumption, is proposed to research the energy optimization problem of two-speed electric vehicles. Firstly, a battery life model that adapts to vehicles under high dynamic conditions is introduced. Then, the speed optimal control problem of the two-speed electric vehicles in the acceleration–cruise–deceleration process is established and solved. Finally, the simulation results of two different performance indicators are contrasted and the performance improvement of the two-speed gearbox to the electric vehicles is analyzed. The simulation results under various working scenarios and driving cycles demonstrate that, compared with the conventional economic indicator considering the energy consumption only, the proposed economic indicator can significantly improve the battery life. In addition, it can also be seen that, compared with the one-speed electric vehicles, the application of a two-speed gearbox provides better performance from the aspects of battery aging saving and energy consumption.

Smart Micro-Grid Performance using Renewable Energy

The aim of this research is to determine the performance of PV panels, wind turbines, battery storage and power imported from the grid to the system which will ensure a reliable energy supply, as well as the technical feasibility of a smart microgrid system. Indonesia’s renewable energy potential for electricity reaches 443 GW, where solar energy is the largest potential, namely 4.8 KWh m–2 or equivalent to 112 000 GWp, but only 10 MWp has been utilized. The most basic problem in this system, namely, the uncertainty of wind energy and solar energy, one of the most vital factors in the optimal size of a renewable energy-based smart microgrid system is the reliability of the system being built. The method used in this research is to collect data on the availability of wind energy and solar energy as well as load analysis on the smart microgrid system. As a result, the resulting power output was 6.2 MWh during the experiment. The highest average Performance Ratio (PR) of the solar energy power generation system, namely 77 % in February 2020. Optimized with Battery Life (OBL) model produces a power output of 102.4 kWh and has an overall system efficiency of 81.92 %.

A Data-Driven Power Management Strategy for Plug-In Hybrid Electric Vehicles Including Optimal Battery Depth of Discharging

For hybrid electric vehicles, higher depth of discharge (DOD) indicates more use of battery energy, which can supply more inexpensive propulsions than the fossil fuel but accelerate the battery aging, thus leading to the increase in the equivalent battery life loss cost (EBLLC) related to battery aging. While developing an energy management strategy considering the battery aging effect for plug-in hybrid electric vehicles (PHEVs), a tradeoff between energy consumption cost (ECC) and EBLLC should be made to identify the optimal DOD and minimize the total cost (TC). Furthermore, the optimal DOD is changeable with the initial state of charge (SOC) level. To develop a robust controller to deal with varying initial SOCs for PHEVs, this paper proposes a data-driven method, namely, a three-layer artificial neural network (ANN) to realize real-time power distribution including battery life model. Real-world speed profiles and Pontryagin's minimum principle (PMP) are leveraged to identify the optimal DODs and generate the neural network training data based on cases with a range of initial SOCs. The results clearly demonstrate the robustness of the proposed ANN and also indicate that the data-driven method can effectively reduce the total of ECC and EBLLC compared to typical optimization algorithms without a battery aging model, including the dynamic programming, PMP, and the rule-based strategy. In particular, the ANN can reduce the TC by 19.99%, 25.97%, and 33.13%, respectively, for cases with the initial SOC of 0.95, 0.85, and 0.65, compared to the rule-based method. And the TC of the ANN is comparable to the PMP including the battery degradation model. Moreover, the training sample scale on forecasting accuracy and computational efficiency of the ANN is evaluated. Finally, the computational time of these methods is comprehensively discussed to evaluate the time efficiency of the proposed method.

Acceleration Speed Optimization of Intelligent EVs in Consideration of Battery Aging

A speed optimization framework is presented to minimize both the battery aging and the energy consumption for intelligent electric vehicles (EVs) during acceleration process. To describe quantitatively the battery capacity loss and to optimize in real-life driving conditions, a control-oriented battery life model is derived. Then, the formulation of the speed optimization during an acceleration process is established and solved by sequential quadratic programming (SQP) algorithm. Several simulations are conducted in the case that an intelligent EV speeds up to the specified speed considering different road slopes. The results during an acceleration process from 0 to 100 km/h within 14 s show that the loss of battery capacity can be reduced by 9.6% while the battery energy consumption is merely increased by 1.6% compared with the strategy that only considers the optimal energy consumption.

Acceleration Velocity Trajectory Optimization of Intelligent EVs Using Battery Life Model

In this paper, taking an intelligent electric vehicle as the research object, mathematical models are firstly built for calculating the percentage of lithium-ion battery capacity loss and the internal resistance increase. Based on the model established, a control-oriented battery life model is derived using to calculate the battery capacity loss during an acceleration process. Then, a velocity trajectory optimization framework is presented to minimize the battery aging life for intelligent EVs during an acceleration process and the problem is solved by SQP algorithm. Finally, according to the simulation results, it can be concluded that the energy consumption per meter is 5.50kJ/m from 0 to 100km/h within 10s. The effect on battery capacity is much greater than that on battery internal resistance during the acceleration process.

Lithium-ion battery aging mechanisms and life model under different charging stresses

Abstract The charging time-consuming and lifespan of lithium-ion batteries have always been the bottleneck for the tremendous application of electric vehicles. In this paper, cycle life tests are conducted to reveal the influence of different charging current rates and cut-off voltages on the aging mechanism of batteries. The long-term effects of charging current rates and cut-off voltages on capacity degradation and resistance increase are compared. The results show that there exists a critical charging current and a critical charging cut-off voltage. When the charging stress exceeds the critical value, battery degradation speed will be greatly accelerated. Furthermore, battery aging mechanisms at various charging currents and cut-off voltages are investigated using incremental capacity analysis. It is indicated that charging current and cut-off voltage should be reduced to retard battery degradation when the battery degrades to a certain extent. The time when the loss of electrode material accelerates is taken as the crisis to reduce charging current and the time when the loss of lithium inventory accelerates is taken as the crisis to reduce charging cut-off voltage. Moreover, an experiential model quantitatively describing the relationship between capacity degradation rate and charging stresses at different aging states is established.

Impact of control strategy on battery degradation for a plug-in hybrid electric city bus in China

Series-parallel Plug-In Hybrid Electric Vehicle combine the advantages of series and parallel configurations and have been used in China. However, battery degradation in series-parallel Plug-In Hybrid Electric city bus applications still need to be investigated. In this paper, a simulation model is developed to simulate a series-parallel Plug-In Hybrid Electric city bus. The simulation model was validated experimentally and shown to agree well with the real system. Additionally, a semi-empirical battery life model was also developed and validated to estimate the battery degradation. According to the simulation model and battery life model, the impact of different control strategies for series-parallel Plug-In Hybrid Electric city buses on battery degradation was investigated. The simulation results showed that series-parallel Plug-In Hybrid Electric city buses with the Maximum Efficiency Control Strategy for series mode and Power Follower Control Strategy for parallel mode reduced battery degradation significantly.

An electric vehicle’s battery life model under car-following model

Using the electricity consumption theory, we in this paper propose an electric vehicle’s battery life model. The numerical results illustrate that the proposed model can qualitatively describe the impacts of the micro-driving behavior on the number of times that the electric vehicle’s battery can cycle under two typical traffic situations. In addition, the numerical results show that the micro-driving behavior will influence the electric vehicle’s battery life, i.e., under the smooth driving behavior, the number of times that the electric vehicle’s battery cycles are stable and the number of the battery cycles will be increased, so the electric vehicle’s battery life can be prolonged.

Optimization‐based power management of a wind farm with battery storage

ABSTRACTThis paper presents an optimization‐based control strategy for the power management of a wind farm with battery storage. The strategy seeks to minimize the error between the power delivered by the wind farm with battery storage and the power demand from an operator. In addition, the strategy attempts to maximize battery life. The control strategy has two main stages. The first stage produces a family of control solutions that minimize the power error subject to the battery constraints over an optimization horizon. These solutions are parameterized by a given value for the state of charge at the end of the optimization horizon. The second stage screens the family of control solutions to select one attaining an optimal balance between power error and battery life. The battery life model used in this stage is a weighted Amp‐hour throughput model. The control strategy is modular, allowing for more sophisticated optimization models in the first stage or more elaborate battery life models in the second stage. The strategy is implemented in real time in the framework of model predictive control. Copyright © 2012 John Wiley & Sons, Ltd.

Cycle-life model for graphite-LiFePO 4 cells

In this report, cycling induced capacity fade of a LiFePO 4 battery was studied and cycle-life models were established. Cell life data for establishing the model were collected using a large cycle-test matrix. The test matrix included three parameters, temperature (−30 to 60 °C), depth of discharge (DOD) (90–10%), and discharge rate (C-rate, ranging from C/2 to 10C, with the 1C rate corresponding to 2A). At the low C-rates, experimental results indicated that the capacity loss was strongly affected by time and temperature, while the DOD effect was less important. At the high C-rates, the charge/discharge rate effects became significant. To establish a life model, we adopt a power law equation in which the capacity loss followed a power law relation with time or charge throughput while an Arrhenius correlation accounted for the temperature effect. This model, when parameters were allowed to change with C-rates, was found to represent a large array of life cycle data. Finally, we discuss our attempts in establishing a generalized battery life model that accounts for Ah throughput (time), C-rate, and temperature.