Online estimation of model parameters and state-of-charge of LiFePO4 batteries in electric vehicles

The accurate estimation of internal parameters and state-of-charge (SoC) of battery, which greatly depends on proper models and corresponding high-efficiency, high-accuracy algorithms, is one of the critical issues for the battery management system. A model-based online estimation method of a LiFePO₄ battery is presented for application in electric vehicles (EVs) by using an adaptive extended Kalman filter (AEKF) algorithm. The Thevenin equivalent circuit model is selected to model the LiFePO₄ battery and its mathematics equations are deduced to some extent. Additionally, an implementation of the AEKF algorithm is elaborated and employed for the online parameters’ estimation of the LiFePO₄ battery model. To illustrate advantages of the online parameters’ estimation, a comparison analysis is performed on the terminal voltages between the online estimation and the offline calculation under the Hybrid pulse power characteristic (HPPC) test and the Urban Dynamometer Driving Schedule (UDDS) test. Furthermore, an efficient online SoC estimation approach based on the online estimation result of open-circuit voltage (OCV) is proposed. The experimental results show that the online SoC estimation based on OCV-SoC can efficiently limit the error below 0.041.     

A wavelet transform‐adaptive unscented Kalman filter approach for state of charge estimation of LiFePo4 battery

LiFePo₄ battery is widely used in electric vehicles; however, its flatness and hysteresis of the open‐circuit voltage curve pose a big challenge to precise state of charge (SOC) estimation. The issue is discussed and addressed in this paper. First, a cell model with hysteresis is built to describe real‐time dynamic characteristics of the LiFePo₄ battery. Second, the model parameters and SOC are estimated independently to avoid the possibility of cross interference between them. For model identification, an adaptive unscented Kalman filter (AUKF) algorithm is used to identify the cell parameters as they change slowly. While SOC could change rapidly, wavelet transform AUKF algorithm is put forward to estimate SOC. In the novel algorithm, the measurement noise can be estimated and updated online. Finally, the performance of the proposed method is verified under dynamic current condition. The experimental results show that estimated value based on the proposed method is more accurate than unscented Kalman filter‐based method and AUKF‐based algorithm. Meanwhile, the proposed estimator also has the merits of fast convergence and good robustness against the initialization uncertainty.     

Cathode material influence on the power capability and utilizable capacity of next generation lithium-ion batteries

Lithium-ion cells (Li-ion) comprising lithium iron phosphate (LiFePO₄) based cathode active material are a promising battery technology for future automotive applications and consumer electronics in terms of safety, cycle and calendar lifetime and cost. Those cells comprise flat open circuit voltage (OCV) characteristics and long-term load history dependent cell impedance. In this work the special electric characteristics of LiFePO₄ based cells are elucidated, quantified and compared to Li-ion cells containing a competing cathode technology. Through pulse tests and partial cycle tests, performed with various olivine based cells, the cycling history dependency of the internal resistance and therefore on the power capability is shown. Hence, methods are illustrated to quantify this load history impact on the cells performance. Subsequently, methods to achieve a safe battery operation are elucidated. Furthermore strategies are given to obtain reliable information about the cells power capability, taking the mentioned properties into consideration.     

Adaptive estimation of PEMFC stack model parameters - An experimental verification

The growing popularity of using proton-exchange membrane fuel cells (PEMFCs) stacks in stationary, portable, and transportation applications is driving researchers to develop proper dynamic models for PEMFCs. These models are used to accurately capture the electrical characteristics and runtime performance. This work proposes a well-known equivalent circuit model of a battery, to be modified and used as a model for a PEMFC stacks voltage-current characteristics. This model is modified by finding suitable functions to model the open circuit voltage and the series resistance, required to model the electrical performance of a 200-W PEMFC stack. The paper also shows that the existing adaptive parameters estimation (APE) technique for Li-ion battery parameters estimation is also able to estimate parameters of the PEMFC stack's model. The model parameters are estimated using the APE technique that requires only five experiments. The model is validated experimentally under different load conditions for a 200-W PEMFC stack supplied from a hydrogen cylinder (voltage error ?0.2 V to 0.5 V), and a 30-W PEMFC stack supplied from a fuel stick (voltage error ?0.2 V–0.4 V). The results show that the parameters estimation methodology works well across PEMFC stacks of different sizes with different input fuel intake configurations, with a minimal terminal voltage estimation error in the order of millivolts. Open circuit voltage measurements (OCV) show that the OCV curve starts at a little lower than 31 V, declines slowly to around 30 V for a normalized hydrogen flow rate of 0.6, after which there is a sudden linear decline in OCV was observed. Most of the data has absolute estimation error less than 0.1 V. In fact, the terminal voltage estimation error across all tests, with different current discharge profiles, lies between ?0.2 and 0.2 V only. Also, 95.84% of the error samples lie between ±0.1% error.     

Research on parameter identification and state of charge estimation of improved equivalent circuit model of Li-ion battery based on temperature effects for battery thermal management

The performance and parameters of Li-ion battery are greatly affected by temperature. As a significant battery parameter, state of charge (SOC) is affected by temperature during the estimation process. In this paper, an improved equivalent circuit model (IECM) considering the influence of ambient temperatures and battery surface temperature (BST) on battery parameters based on second-order RC model have been proposed. The exponential function fitting (EFF) method was used to identify battery model parameters at 5 ambient temperatures including −10°C, 0°C, 10°C, 25°C and 40°C, fitting the relationship between internal resistance and BST. Then, the SOC of the IECM was estimated based on the extended Kalman filter (EKF) algorithm. Using the result calculated by the Ampere-hour integration method as the standard, the data of battery under open circuit voltage (OCV) test profile and dynamic stress test (DST) profile at different ambient temperatures has been compared with the ordinary second-order RC model, and the advantages of the SOC estimation accuracy with IECM was verified. The numerical results showed that the IECM can improve the estimation accuracy of battery SOC under different operating conditions.     

State‐of‐charge estimators considering temperature effect,hysteresis potential,and thermal evolution for LiFePO4 batteries

To achieve accurate state‐of‐charge (SoC) estimation for LiFePO₄ batteries, the effects of temperature, hysteresis, and thermal evolution are elaborately modeled. Open‐circuit voltage is regarded as the sum of electromotive force and hysteresis potential (V_h), where electromotive force is constructed as the function of SoC and temperature and V_h is reproduced with a geometrical model. By simulating battery heat generation and dissipation, a thermal evolution model is established and exploited for open‐circuit voltage and parameter identification. Then, on the basis of a second‐order equivalent circuit model, 2 SoC estimation schemes are proposed: One scheme uses the recursive least square with forgetting factor algorithm and off‐line equivalent circuit model parameters derived by the differential evolution algorithm; the other scheme resorts to the adaptive extended Kalman filter (EKF) and online tuned parameters. Experiments validate the effectiveness of the hysteresis model and the thermal evolution model. In contrast to a joint EKF estimator, experimental results under different temperatures and initial states suggest that both the proposed estimators are superior to the joint EKF estimator. Benefiting from the online updated parameters, the adaptive EKF estimator behaves best for giving consistent SoC‐tracking performance under different conditions.     

Composite electrodes of disordered carbon and graphite for improved battery state estimation with minimal performance penalty

Voltage based state of charge (SOC) estimation is challenging for lithium ion batteries that exhibit little open circuit voltage (OCV) change over a large SOC range. We demonstrate that by using a composite negative electrode composed of disordered carbon and graphite, we were able to introduce additional features to the OCV-SOC relationship that facilitate voltage-based SOC estimation. In contrast to graphite, the potential of disordered carbon is sensitive to the state of charge; this behavior, when manifested in a lithium ion battery, gives rise to additional beneficial features of the cell OCV-SOC relationship in terms of state estimation. We have demonstrated the effectiveness of the approach by comparing model simulations and corresponding experimental data of a cell composed of LiFePO₄ positives and graphite + disordered carbon composite negative electrodes. Last, we find that although the graphite material has a higher coulombic capacity, very little (dynamic) performance loss is manifest with the mixed graphite + disordered carbon composite is employed.     

Model‐based unscented Kalman filter observer design for lithium‐ion battery state of charge estimation

Accurate battery state‐of‐charge is essential for both driver notification and battery management units reliability in electric vehicle/hybrid electric vehicle. It is necessary to develop a robust state of charge (SOC) estimation approach to cope with nonlinear dynamic battery systems. This paper proposed an estimation method to identify the SOC online based on equivalent circuit battery model and unscented Kalman filter technique. Firstly, the parameters of dynamic battery model are identified offline and validated through typical electric vehicle road operation to guarantee its precision. Then the performance with respect to converge time, observer accuracy, robustness against system modeling errors, and mismatched initial SOC guess values is investigated. The accuracy of proposed estimation algorithm is validated under improved hybrid power pulse characterization test and New European Driving Cycle. Experiment and numerical simulation results clearly demonstrate that the proposed method is highly reliable with good robustness to different operating conditions and battery aging.     

Battery open-circuit voltage estimation by a method of statistical analysis

The basic task of a battery management system (BMS) is the optimal utilization of the stored energy and minimization of degradation effects. It is critical for a BMS that the state-of-charge (SoC) be accurately determined. Open-circuit voltage (OCV) is directly related to the state-of-charge of the battery, accurate estimation of the OCV leads to an accurate estimate of the SoC. In this paper we describe a statistical method to predict the open-circuit voltage on the basis of voltage curves obtained by charging batteries with different currents. We employ a dimension reduction method (Karhunen–Loeve expansion) and linear regression. Results of our modelling approach are independently validated in a specially designed experiment.     

Thermal modeling of a cylindrical LiFePO4/graphite lithium-ion battery

A lumped-parameter thermal model of a cylindrical LiFePO₄/graphite lithium-ion battery is developed. Heat transfer coefficients and heat capacity are determined from simultaneous measurements of the surface temperature and the internal temperature of the battery while applying 2 Hz current pulses of different magnitudes. For internal temperature measurements, a thermocouple is introduced into the battery under inert atmosphere. Heat transfer coefficients (thermal resistances in the model) inside and outside the battery are obtained from thermal steady state temperature measurements, whereas the heat capacity (thermal capacitance in the model) is determined from the transient part. The accuracy of the estimation of internal temperature from surface temperature measurements using the model is validated on current-pulse experiments and a complete charge/discharge of the battery and is within 1.5 °C. Furthermore, the model allows for simulating the internal temperature directly from the measured current and voltage of the battery. The model is simple enough to be implemented in battery management systems for electric vehicles.     

Analysis of polymer electrolyte fuel cell performance by electrode polarization model

For development of polymer electrolyte fuel cell (PEFC) lifetime estimation method, a high accuracy PEFC electrode polarization model is required. An electrode polarization model which was previously proposed was verified. However, accuracy of the electrode polarization model was not enough to estimate PEFC performance under various conditions. A new high accuracy PEFC electrode polarization model has been developed based on electrochemical consideration and data observed at elevated pressures. In the cathode polarization model, effects of O₂ diffusion and H₂O plugging have to be considered to obtain high accuracy for long-term operation. In addition, PEFC performance degradation was analyzed by the electrode polarization model. Main factors of PEFC performance degradation are OCV drop, the cathodic activation polarization, voltage drops by O₂ diffusion and H₂O plugging.     

Online estimation of internal resistance and open-circuit voltage of lithium-ion batteries in electric vehicles

State-of-charge (SoC) and state-of-health (SoH) define the amount of charge and rated capacity loss of a battery, respectively. In order to determine these two measures, open-circuit voltage (OCV) and internal resistance of the battery are indispensable parameters that are obtained with difficulty through direct measurement. The motivation of this study is to develop an online, simple, training-free, and easily implementable scheme that is capable of estimating such parameters, particularly for the lithium-ion battery in battery-powered vehicles. Based on an equivalent circuit model (ECM), the electrical performance of a battery can be formulated into state-space representation. Also, underdetermined model parameters can be arranged to appear linearly so that an adaptive control approach can be applied. An adaptation algorithm is developed by exploiting the Lyapunov-stability criteria. The OCV and internal resistance can be extracted exactly without limitations of a system input signal, such as persistent excitation (PE), enhancing the method applicability for vehicular power systems. In this study, both simulations and experiments are established to verify the capability and effectiveness of the proposed estimation scheme.     

An SOE estimation model considering electrothermal effect for LiFePO4/C battery

The state of energy (SOE) is an important performance parameter and evaluation index for LiFePO₄/C battery since the available energy can be known more intuitively through SOE compared with state of charge (SOC). First, in order to improve the estimation accuracy of SOE, a novel estimation model combining electrical energy and thermal energy is put forward by studying the effects of discharge rate to the change laws of all kinds of energy inside the battery cell. Moreover, the concepts of unavailable energy E_u, maximum allowable energy E, and discharge energy efficiency η are originally proposed based on the analysis of energy consumption. Second, the parameter of actual maximum energy and energy consumption revised by the case of LiFePO₄/C battery can give an example to show the specific steps for improving the estimation accuracy of SOE during any integration time by using the novel SOE estimation model. Lastly, 2 international standard test experiments of EV are conducted to show the correction of SOC can efficiently limit the error below 4.6% and also indicate the novel SOE estimation method suitable for application area.     

An enhanced temperature-dependent model and state-of-charge estimation for a Li-Ion battery using extended Kalman filter

Development of high-fidelity mathematical models and state-of-charge (SOC) estimation of Li-ion battery becomes a significant challenge when the temperature effects are considered. In this paper, we propose an enhanced temperature-dependent equivalent circuit model for a Li-ion battery and applied it for battery parameters estimation and model validation, as well as SOC estimation. First, the new battery model is elaborated, including a newly integrated resistance-capacitor structure, a static hysteresis voltage and a temperature compensation voltage term. The forgetting factor least square approach is utilized to realize the parameter identification. Next, the proposed battery model is employed to estimate battery SOC by incorporating the extended Kalman filter algorithm. Finally, simulation results are provided to demonstrate the superior performance of the proposed battery model in comparison with the common first-order Thevenin temperature model. Compared with Thevenin model, the maximal values of relative reconstruction error and root mean squared error with the proposed battery model are decreased by about 33.3% and 50.0%, respectively, for the battery terminal output voltage, 50.0% and 53.0%, respectively, for the SOC estimation, under three different test profiles.     

Mechanically alloyed Mg2Ni for metal-hydride–air secondary battery

Mechanically alloyed Mg₂Ni and a single air (oxygen) electrode are used as the anode and cathode, respectively, in a Mg₂Ni|6 M KOH|O₂ rechargeable metal-hydride–air (MH–air) battery. The battery is tested for self-discharge by measuring the open-circuit voltage (OCV) and cycling characteristics. Battery degradation after charge–discharge cycling is characterized by means of X-ray diffraction (XRD) and scanning electron microscopic (SEM) analyses.     

Review of lithium-ion battery state of charge estimation

The technology deployed for lithium-ion battery state of charge (SOC) estimation is an important part of the design of electric vehicle battery management systems. Accurate SOC estimation can forestall excessive charging and discharging of lithium-ion batteries, thereby improving discharge efficiency and extending cycle life. In this study, the key lithium-ion battery SOC estimation technologies are summarized. First, the research status of lithium-ion battery modeling is introduced. Second, the main technologies and difficulties in model parameter identification for lithium-ion batteries are discussed. Third, the development status and advantages and disadvantages of SOC estimation methods are summarized. Finally, the current research problems and prospects for development trends are summarized.     

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.     

Li-ion battery state of health estimation through Gaussian process regression with Thevenin model

This paper proposes a model-based and data-driven joint method to estimate the state of health of Li-ion batteries. To accurately quantify battery degradation, a novel resistance-based aging feature is defined from the Thevenin model, and the defined aging feature is approximately linear with capacity degradation. An orthogonal experimental design and a two-way analysis of variance are used to validate the robustness of the defined aging feature. Considering the influence of temperature on battery performance, Box-Cox transformation is introduced to improve the aging feature linearity at low temperatures. Then, an estimator for state of health is established by using Gaussian process regression. Battery aging experiments are conducted to illustrate the estimation effect of the proposed method. The experimental results show that the proposed method has high estimation accuracy at different temperatures. Using the same aging feature, the backpropagation network and support vector regression are implemented to verify the generality of the estimation framework.     

Experimental research on temperature rise and electric characteristics of aluminum air battery under open‐circuit condition for new energy vehicle

Due to lack of systematic research on open‐circuit voltage (OCV) and electrolyte temperature rise characteristics of aluminum air battery, in order to explore the influential factors on the OCV and electrolyte temperature rise of aluminum air battery, in this paper, for the first time, we studied the effects of different ambient temperature conditions, different concentrations of NaOH and KOH electrolyte, and pure aluminum and aluminum alloy on the OCV and electrolyte temperature rise of aluminum air battery. Results show that the OCV of aluminum air battery is obviously affected by ambient temperature conditions, electrolyte concentration, and different anode materials. The OCV range is 1.5 to 1.8 V at 0°C under different KOH‐electrolyte concentrations when aluminum alloy is used as anode material; with the increase of ambient temperature, the OCV will rise, and the range is 1.8 to 1.95 V. The working process of aluminum air battery is accompanied by the phenomenon of heat release, and the temperature rise range of electrolyte will not exceed 7°C when aluminum alloy is used as the anode material; however, the highest temperature of the electrolyte can reach 100°C when pure aluminum is used as the negative electrode material. The results of this study will provide theoretical guidance for designing aluminum air batteries and identifying their optimal operating conditions.