Li‐ion battery dynamics model parameter estimation using datasheets and particle swarm optimization

Dynamics modeling is of fundamental importance to Li‐ion battery design and manufacturing. Accurate dynamics models established can be used to optimize the operation strategy, manage the life cycle, and thus ensure the economic and safe operation of the batteries. The Li‐ion dynamics model examined in this paper has integrated both empirical and electrochemical aspects, and it has been specifically validated for electric vehicle applications using experimental data. Previously, the model parameter estimation was done by manually picking three key points from the discharge curve obtained from the datasheet. The approach is quite subjective and error prone. The resulted model may deviate greatly from the experimental curve. To address this issue, this paper proposes to use particle swarm optimization to more objectively estimate the model parameters. Results from case studies show that the proposed approach provides more accurate estimation of the true parameters, and thus the new approach can more precisely capture the battery dynamics. In addition, this approach is generic because it is independent of specific battery chemistries and applicable to many different types of Li‐ion batteries. Copyright © 2016 John Wiley & Sons, Ltd.     

Reduced‐order modeling of lead‐acid battery using cluster analysis and orthogonal cluster analysis method

Real‐time fast simulation of lead‐acid battery (LAB) plays an important role in monitoring, control, optimization, and many other engineering fields. Hence, any improvement toward a reduction in computational time of LAB simulation while maintaining the accuracy of results is of practical interest. Reduced‐order modeling (ROM) is one of the promising tools, which is computationally cost‐effective along with producing accurate results. In this study, ROM is employed in a transient one‐dimensional simulation of LABs within discharge to investigate the variation of battery parameters, eg, cell voltage, acid concentration, and state of charge (SoC). Accordingly, three reduced‐order models are implemented, namely, proper orthogonal decomposition (POD), cluster analysis (CA), and orthogonal cluster analysis (OCA), wherein the latter one is a new hybrid model of POD and CA methods proposed in the present work. The results reveal that ROM of LAB reduces the simulation time significantly (speed‐up factor about 7‐12) and provide good consistency comparing with previous experimental and numerical studies (less than 1% relative error for cell voltage, acid concentration, and SoC). In addition, the results indicate that the new hybrid method inherits the advantages of both POD and CA methods, ie, enhances the speed of POD method by 8% to 24% and accuracy of CA method by 17% to 65%.     

A new dynamic SOH estimation of lead‐acid battery for substation application

State of Health (SOH) is one of the most important parameters of lead‐acid batteries. Most of the existing SOH estimation methods only take the influence of charge cycles into consideration, and the estimation accuracy is limited. Batteries in the substations have two typical states: one is the check‐discharge state, in which the batteries are discharged for 8 h at 0.1 C (Capacity) to determine whether the battery pack has certain reliability. The other is the floating charge state, in which the batteries are connected to the charger to maintain full power. This paper proposes a novel SOH estimation method based on the two states. In the check‐discharge state, the relationship between the voltage and the age of battery is analysed. The health index, which is introduced in this model, is affected by the age of battery. In the floating state, the relationship between the internal resistance and the age of battery is discussed. Another SOH model is established based on the change of the internal resistance. By combining the two models, the estimation method can achieve real‐time estimation and high accuracy for substation application. An accelerated life test is applied to verify the theoretical analysis. The experimental results demonstrate that the SOH estimation error is less than 3% which is very satisfactory for practical applications. Copyright © 2016 John Wiley & Sons, Ltd.     

Subspace‐based modeling and parameter identification of lithium‐ion batteries

For reliable and safe operation of lithium‐ion batteries in electric vehicles, the monitoring of state‐of‐charge and state‐of‐health is necessary. However, these internal states cannot be measured directly, which are usually estimated through model‐based techniques. Therefore, an accurate application‐oriented battery model is of significant importance. The purpose of this paper is to present a novel method on battery modeling and parameter identification. In this work, a state‐space model with clear mathematical and electrochemical meanings is proposed on the basis of the electrochemical basics of lithium‐ion batteries. The frequency‐domain characteristics of the lithium‐ion batteries are also investigated. On the basis of the frequency analysis, an identification test profile that can excite the dynamic characteristics of the battery fully and persistently is proposed. A subspace‐based algorithm is then adopted to identify the parameters of the battery model. The performance and robustness of the estimated model are validated through some experiments and simulations. The validation results show that the proposed method can achieve an acceptable accuracy with the maximum error being less than 2%. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental validation for Li-ion battery modeling using Extended Kalman Filters

The battery management systems (BMS) is an essential emerging component of both electric and hybrid electric vehicles (HEV) alongside with modern power systems. With the BMS integration, safe and reliable battery operation can be guaranteed through the accurate determination of the battery state of charge (SOC), its state of health (SOH) and the instantaneous available power. Therefore, undesired power fade and capacity loss problems can be avoided. Because of the electrochemical actions inside the battery, such emerging storage energy technology acts differently with operating and environment condition variations. Consequently, the SOC estimation mechanism should cope with the probable changes and uncertainties in the battery characteristics to ensure a permanent precise SOC determination over the battery lifetime.This paper aims to study and design the BMS for the Li-ion batteries. For this purpose, the system mathematical equations are presented. Then, the battery electrical model is developed. By imposing known charge/discharge current signals, all the parameters of such electrical model are identified using voltage drop measurements. Then, the extended kalman filter (EKF) methodology is employed to this nonlinear system to determine the most convenient battery SOC. This methodology is experimentally implemented using C language through micro-controller. The proposed BMS technique based on EKF is experimentally validated to determine the battery SOC values correlated to those reached by the Coulomb counting method with acceptable small errors.     

Computational study about the effect of electrode morphology on the performance of lithium‐ion batteries

Electrode morphology has significant influence on the performance of lithium‐ion batteries in that it controls electrical conductivity and electrode utilization by establishing electrical connectivity in the electrode. The present study investigates the effect of the electrode morphology on battery performance by combining two different mathematical models. First, a two‐dimensional, direct numerical simulation (DNS) model is introduced, which stochastically generates electrode morphology and calculates electrical conduction and electrode utilization. Various simulations are conducted to evaluate the effect of the active particle coating, conductive agent loading, particle size, and electrode compression by using the DNS model. Second, data acquired from the DNS model are applied to the blended‐electrode model to evaluate battery performance. Calculation result confirms that electrode morphologies have significant effects on both capacity and power of lithium‐ion batteries. Copyright © 2016 John Wiley & Sons, Ltd.     

A review of novel thermal management systems for batteries

In the recent years, significant developments in the electric batteries have made them one of the most promising storage technologies for electrical energy. Among the various rechargeable batteries that are developed, lithium ion batteries stand out due to their capability of storing more energy per unit mass, low discharge rate, low weight, and lack of a memory effect. The advantages that batteries offer have promoted the development of the electric and hybrid electric vehicles. However, during charging and discharging processes, batteries generate heat. If this heat is not removed quickly, the battery temperature will rise, resulting in safety concerns and performance degradation. Thermal management systems are developed to maintain the temperature of the battery within the optimum operation range. This review paper focuses on novel battery thermal management systems (BTMSs). Air, liquid, phase change material, and pool‐based BTMSs are considered. Air‐based thermal management systems are discussed first. Liquid cooling systems and phase change‐based systems are discussed subsequently, and then the recently proposed evaporating pool‐based thermal management system is considered.     

Single and multi‐objective optimization for the performance enhancement of lead–acid battery cell

Electric energy storage systems are used considerably in industries and daily applications. The demand for batteries with high energy content has increased because of their use in hybrid vehicles. Lead–acid batteries have wide applications because of their advantages such as high safety factor and low cost of production. The major shortcoming of lead–acid batteries is low energy content and high dimension and weight. Nowadays, a common method to increase the energy content of lead–acid battery is the experimental method with trial and error, which is time consuming and expensive. In this paper, non‐isothermal one‐dimensional numerical simulation of lead–acid battery with finite volume method is performed. In addition, a cell with higher energy content and lower thickness is designed by using particle swarm optimization algorithm based on developed simulation code. The results of single objective optimization show that an optimal battery that has 27.6% higher energy can be made with the same cell dimension. The results also show that an optimum cell battery can be obtained with a decrease of 24% in thickness while keeping the energy the same. Moreover, a multi‐objective optimization algorithm is utilized to find Pareto optimal solutions while considering the energy content and thickness objectives simultaneously. Copyright © 2016 John Wiley & Sons, Ltd.     

High-performance solid-state metal-air batteries with an innovative dual-gel electrolyte

An innovative dual-gel electrolyte design is proposed in this work for solid-state metal-air batteries, which utilizes the acid-alkaline dual-gel for the Al-air and Zn-air batteries, and the acid-salt dual-gel for the Mg-air battery. During battery storage, a plastic thin-film can be used for dual-gel separation, which can be removed before battery usage. And during battery working, benefited from the higher ionic diffusion resistance of gel electrolytes, the mixing of different electrolytes is significantly reduced without using complex flowing system or expensive bipolar membrane separator, ensuring a pseudo-stable battery system. The acid-alkaline dual-gel Al-air and Zn-air batteries can provide ～0.5 V higher voltage output than the corresponding alkaline single-gel batteries, and the discharge lifetime is not compromised too much due to the effective suppression of acid-alkaline neutralization. As for the acid-salt dual-gel Mg-air battery, attributed to the Mg(OH)₂ dissolution by crossovered acid, both a 0.65 V higher discharge voltage and a 5.5 times longer discharge lifetime are achieved compared with the salt single-gel battery. By simulating the variation of ion concentration inside gels during battery discharge, it is found that the effective ion diffusivity in gel plays a vital role in the battery stability. In general, a moderate value is favored to avoid both the ion shortage at the electrode-electrolyte interface and the vigorous neutralization at the gel-gel contact surface. Furthermore, a flexible version of the dual-gel metal-air battery is demonstrated by using paper-based gel electrolytes.     

Mathematical modeling of lithium-ion and nickel battery systems

A review of mathematical models of lithium and nickel battery systems developed at the University of South Carolina is presented. Models of Li/Li-ion batteries are reviewed that simulated the behavior of single electrode particles, single electrodes, full cells and batteries (sets of full cells) under a variety of operating conditions (e.g. constant current discharge, pulse discharge, impedance and cyclic voltammetry). Models of nickel battery systems are reviewed that simulate the performance of full cells, as well as the behavior of the nickel hydroxide active material. The ability of these models to predict reality is demonstrated by frequent comparisons with experimental data.     

Estimation of battery available capacity under variable discharge currents

In this paper, a new mathematical model in semi-empirical form for lead-acid batteries is presented, which describes the relationship between the battery terminal voltage and the variable discharge current. Based on the proposed model, a new estimation method of the battery available capacity (BAC) in the presence of variable discharge currents is developed. The method involves the real-time identification of the model parameters which are then used to estimate the BAC according to the predefined cutoff voltage and the trend of battery terminal voltage during discharging. Thus, both temperature and aging influences on the BAC are considered inherently. Comparisons between the calculated results and the measured data confirm that the proposed method can provide an accurate real-time estimation of the BAC under variable discharge currents.     

Determination of state-of-charge and state-of-health of batteries by fuzzy logic methodology

A practical method of predicting state-of-charge (SOC) and state-of-health (SOH) of battery systems has been developed and tested for several systems. The method involves the use of fuzzy logic mathematics to analyze data obtained by impedance spectroscopy and/or coulomb counting techniques. Fuzzy logic provides a powerful means of modeling complex, non-linear systems without the need for explicit mathematical models. New detailed impedance date has been obtained on the discharge performance of primary lithium/sulfur dioxide cells. Earlier data, obtained by Rutgers co-workers on nickel/metal hydride and other systems, have been reviewed and re-interpreted using fuzzy logic methodology. Devices are being developed for several systems, which will predict the SOC and SOH of batteries without the need to know their previous discharge and/or cycling history.     

Dynamic model of a lead acid battery for use in a domestic fuel cell system

This paper presents a review of existing dynamic electrical battery models and subsequently describes a new mathematical model of a lead acid battery, using a non-linear function for the maximum available energy related to the battery discharge rate. The battery state of charge (SOC) is expressed in a look-up table relative to the battery open circuit voltage (VOC). This look-up table has been developed through low discharge experiments of the battery modelled. Further, both the internal resistance and self-discharge resistance of the battery are subsequently expressed as functions of the open circuit voltage. By using an electrical model with these characteristics and a temperature compensation element to model different rates of charge and discharge, a relatively simple and accurate battery model has been developed.The new model takes into account battery storage capacity, internal resistance, self-discharge resistance, the electric losses and the temperature dependence of a lead acid battery. It is shown in this paper how the necessary parameters for the model were found. The battery modelled was a Hawker Genesis 42 Ah rated gelled lead acid battery.The simulation results of the new model are compared with test data recorded from battery discharge tests, which validate the accuracy of the new model.     

Hydrogen-absorbing alloys for the NICKEL–METAL hydride battery

In recent years, owing to the rapid development of portable electronic and electrical appliances, the market for rechargeable batteries has increased at a high rate. The nickel-metal hydride battery (Ni/MH) is one of the more promising types, because of its high capacity, high-rate charge/discharge capability and non-polluting nature. This type of battery uses a hydrogen storage alloy as its negative electrode. The characteristics of the Ni/MH battery, including discharge voltage, high-rate discharge capability and charge/discharge cycle lifetime are mainly determined by the construction of the negative electrode and the composition of the hydrogen-absorbing alloy. The negative electrode of the Ni/MH battery described in this paper was made from a mixture of hydrogen-absorbing alloy, nickel powder and polytetrafluoroethylene (PTFE). A multicomponent MmNi₅-based alloy (Mm_0.95Ti_0.05Ni_3.85 Co_0.45Mn_0.35Al_0.35) was used as the hydrogen-absorbing alloy. The discharge characteristics of the negative electrode, including discharge capacity, cycle lifetime, and polarization overpotential, were studied by means of electrochemical experiments and analysis. The decay of the discharge capacity for the Ni/MH battery (AA size, 1 Ah) was about 1% after 100 charge/discharge cycles and 10% after 500 charge/discharge cycles.     

An equivalent circuit model of a deformed Li-ion battery with parameter identification

A new equivalent circuit model (ECM) of a Li-ion battery is developed in this study. The developed model is utilized to obtain the dynamic electrical response of the battery when it is deformed under external force. Compared with other models, this model is developed based on a modified Thevenin model, and the parameters of the developed model are relevant to state of charge, the battery surface temperature, and the deformation. In this study, to obtain the real electrical response of the battery when it deformed under external force, batteries that are compressed by different deformations from 0 to 5 mm are studied with pulse discharging tests. Then, the parameters of the circuit elements are identified by a differential evolution algorithm based on the data obtained from these tests. Moreover, the data from the pulse discharging tests of batteries compressed by 3.5, 4.25, and 4.5 mm and the data from the pulse charging tests of batteries compressed by 0 and 1 mm are used to verify the parameters. The results illustrate that the battery capacity should drop significantly when the battery is severely deformed, but the battery still can be charged and discharged. Most importantly, the discharging curves of these tested deformed batteries are similar to those of undeformed ones. Moreover, the developed new ECM can predict the dynamic electrical response of a deformed battery accurately.     

Coordinated discharge of a collection of batteries

Collections of batteries are used to supply energy to a variety of applications. By utilizing the energy in such a collection efficiently, we can improve the lifetime over which energy can be supplied to the application. We say that the discharge of a collection of batteries is coordinated when, at the end of discharge, the difference in the remaining capacity of individual batteries is small. This paper presents a decision-maker based on a goal-seeking formulation that coordinates the discharge of a collection of batteries. This formulation allows us to use a simple battery model and simple decision-making algorithms. We present results from MATLAB simulations that demonstrate the performance of the decision-maker when energy is drawn out of the collection in three different discharge scenarios. The new decision-maker consistently improves the discharge efficiency obtained using scheduling methods. Our results show that when the discharge is coordinated, the lifetime of the collection is extended.     

Towards real-time (milliseconds) parameter estimation of lithium-ion batteries using reformulated physics-based models

In this paper, transport and kinetic parameters of lithium-ion batteries are estimated using a rigorous porous electrode theory based model. The rigorous model used in this investigation is reformulated using advanced mathematical techniques. Since batteries and other electrochemical devices are used in hybrid environments, which include devices with time constants less than a second (like supercapacitor), we need to develop parameter estimation codes with computation time less than a second or a few milliseconds. In this investigation, the computation time for parameter estimation measures between 100 and 300 ms since a reformulated battery model is devised especially for these purposes. Obtaining the numerical solution for battery model equations is very difficult towards the end of discharge and is usually neglected for parameter estimation purposes. However, in this paper the estimation takes into account the entire discharge data ranging from an initial potential of 4.2 V to a cut-off potential of 2.5 V. It is found from this investigation that the reformulated lithium-ion battery model is efficient and accurate in estimating parameters.     

Reliable battery operation — a challenge for the battery management system

Advanced batteries, like lithium-ion batteries, are more sensitive in case of irregular operation than conventional batteries. Therefore, the operation of such batteries must be controlled by a management system. The features of a battery management system depend on the application, but in most cases, features like battery state determination, electrical management and safety management are necessary. This paper describes these functions of a battery management system. The use of a battery management system will lead to an increased lifetime and a safer operation of the battery.     

Multi‐fault synergistic diagnosis of battery systems based on the modified multi‐scale entropy

Faults of lithium batteries in their early stage in electric vehicles (EVs) are usually undetectable, and their characteristics are difficult to be extracted by conventional methods. This paper presents a novel synergistic diagnosis scheme for multiple battery faults using the modified multi‐scale entropy (MMSE). The proposed MMSE can effectively extract the multi‐scale features of complex battery signals in the early stages of battery faults as well as overcome the shortage of the coarse‐grained mode in the standard multi‐scale entropy. The simulation results on experimental data and the real‐world operational vehicles show that the proposed method can effectively detect and locate multiple battery faults/abnormities before they trigger the alarm thresholds. The defined sensitivity factor can implement real‐time evaluation on abnormities with high efficiency and stability, and the developed variable‐calculation‐window diagnosis scheme can synchronously detect and locate different fault types in real time. Furthermore, feasibility, stability, reliability, versatility, robustness, and practicality of the proposed method are separately verified using multiple sets of real‐world operation data. More importantly, the proposed method also provides feasibility to effectively prevent battery thermal runaway caused by multiple battery abnormities/faults. The applications of multi‐scale entropy theory is the first of its kind to battery fault diagnosis on the real‐world operational vehicles.