Battery Equivalent Circuit Model Research Articles

On-board adaptive model for state of charge estimation of lithium-ion batteries based on Kalman filter with proportional integral-based error adjustment

With the rapid development of battery-powered electric vehicles, the lithium-ion battery plays a critical role in the reliability of vehicle system. In order to provide timely management and protection for battery systems, it is necessary to develop a reliable battery model and accurate battery parameters estimation to describe battery dynamic behaviors. Therefore, this paper focuses on an on-board adaptive model for state-of-charge (SOC) estimation of lithium-ion batteries. Firstly, a first-order equivalent circuit battery model is employed to describe battery dynamic characteristics. Then, the recursive least square algorithm and the off-line identification method are used to provide good initial values of model parameters to ensure filter stability and reduce the convergence time. Thirdly, an extended-Kalman-filter (EKF) is applied to on-line estimate battery SOC and model parameters. Considering that the EKF is essentially a first-order Taylor approximation of battery model, which contains inevitable model errors, thus, a proportional integral-based error adjustment technique is employed to improve the performance of EKF method and correct model parameters. Finally, the experimental results on lithium-ion batteries indicate that the proposed EKF with proportional integral-based error adjustment method can provide robust and accurate battery model and on-line parameter estimation.

Electric vehicle battery parameter identification and SOC observability analysis: NiMH and Li‐S case studies

In this study, battery model identification is performed to be applied in electric vehicle battery management systems. Two case studies are investigated: nickel-metal hydride (NiMH), which is a mature battery technology, and lithium-sulfur (Li-S), a promising next-generation technology. Equivalent circuit battery model parameterization is performed in both cases using the Prediction-Error Minimization algorithm applied to experimental data. Performance of the Li-S cell is also tested based on urban dynamometer driving schedule (UDDS). The identification results are then validated against the exact values of the battery parameters. The use of identified parameters for battery state-of-charge (SOC) estimation is also discussed. It is demonstrated that the set of parameters changes with a different battery chemistry. In the case of NiMH, the battery open circuit voltage (OCV) is adequate for SOC estimation whereas Li-S battery SOC estimation is more challenging due to its unique features such as flat OCV-SOC curve. An observability analysis shows that Li-S battery SOC is not fully observable and the existing methods might not be applicable for it. Finally, the effect of temperature on the identification results and the observability are discussed by repeating the UDDS test at 5, 10, 20, 30, 40 and 50 degree Celsius

Analytic Derivation of Battery SOC Estimation Error under Sensor Noises

It is well recognized that voltage and current sensor noises are one of the major sources of battery state of charge (SOC) estimation errors. However, quantitative relationship between the estimation error and sensing noises remains to be established systematically. This paper is devoted to filling this critical gap by deriving the analytic expression of the SOC estimation error under sensing noises. The considered sensing noises include both bias and variance. The derivation is based on a Kalman filter and an equivalent circuit battery model. The obtained analytic expressions can be conveniently used to evaluate the robustness and reliability of SOC estimation as well as guide observer design.

Total Least Squares State of Charge Estimation for Lithium-Ion Batteries: An Efficient Moving Horizon Estimation Approach

This paper proposes a computationally efficient moving horizon approach for total least squares (TLS) battery state of charge (SOC) estimation. Much of the existing SOC estimation literature assumes that uncertainties arise mainly from (i) unmodeled dynamics and (ii) output measurement noise. In contrast, the total least squares (TLS) estimation problem explicitly examines the added noise affecting both output and input measurements. This increases the computational burden associated with TLS estimation by necessitating input trajectory estimation. We address this challenge by exploiting the differential flatness of a temperature-dependent equivalent circuit battery model to improve the computational speed of TLS estimation. Since the model is differentially flat, one can represent its underlying dynamics in terms of the time history of a single flat output. The exploitation of differential flatness improves the computational efficiency of moving horizon estimation (MHE) in two ways: (i) it decreases the number of decision variables significantly and (ii) eliminates battery dynamics-related equality constraints. A simulation study compares the proposed work to a benchmark unscented Kalman filter (UKF), and shows that the proposed flatness-based MHE framework can provide more accurate SOC estimates.

SoC Estimation of Lithium Battery Based on AEKF Algorithm

Lithium iron phosphate power battery is the research object in this paper, in order to accurately estimate the lithium ion power battery state of charge(SoC). By the research and analysis of traditional lithium ion power battery SoC estimation algorithm, the paper puts forward a kind of algorithm based on Adaptive Extended Kalman Filtering Algorithm of lithium ion power battery SoC estimation algorithm, and puts forward combining PNGV equivalent circuit battery model and AEKF algorithm, using MATLAB to simulate verified the feasibility of the algorithm and estimation accuracy. Simulation and experiment results show that the adaptive extended Kalman filtering algorithm of lithium-ion power battery online estimator is effective, which can accurately estimate the SoC of the battery and has high precision. This algorithm is applicable to the lithium ion power battery SoC estimation.

Battery Internal Short Circuit Detection

Internal short circuit (ISCr) is one of the major safety concerns of lithium batteries, and may result in thermal runaway of batteries. The detection of ISCr in battery is critical for preventing thermal runaway and promoting electrical vehicle safety. In this research, the electrical characteristics of the ISCr of lithium ion batteries are analyzed through the battery equivalent circuit model (ECM). An ISCr detection method is developed based on battery consistency inside the battery pack. The proposed ISCr detection method adopts the recursive least square (RLS) algorithm basing on the mean-difference model (MDM). The proposed method first estimates the basic parameters of the MDM, then calculates the characteristic parameters, such as the differential of the voltage and the fluctuation function of the internal resistance, derived from the basic parameters of the MDM. These characteristic parameters largely vary from their normal values once ISCr occurs, thereby enable the battery management system to achieve ISCr detection. The effectiveness of the proposed method is validated through experiments. The proposed ISCr detection method is integrated into battery management system (BMS) of vehicles and yields satisfactory performance.

A novel method for identification of lithium-ion battery equivalent circuit model parameters considering electrochemical properties

Abstract This paper proposes a novel parameter identification method for the lithium-ion (Li-ion) battery equivalent circuit model (ECM) considering the electrochemical properties. An improved pseudo two-dimension (P2D) model is established on basis of partial differential equations (PDEs), since the electrolyte potential is simplified from the nonlinear to linear expression while terminal voltage can be divided into the electrolyte potential, open circuit voltage (OCV), overpotential of electrodes, internal resistance drop, and so on. The model order reduction process is implemented by the simplification of the PDEs using the Laplace transform, inverse Laplace transform, Pade approximation, etc. A unified second order transfer function between cell voltage and current is obtained for the comparability with that of ECM. The final objective is to obtain the relationship between the ECM resistances/capacitances and electrochemical parameters such that in various conditions, ECM precision could be improved regarding integration of battery interior properties for further applications, e.g., SOC estimation. Finally simulation and experimental results prove the correctness and validity of the proposed methodology.

An Improved Battery On-line Parameter Identification and State-of-charge Determining Method

Abstract To improve the estimation accuracy of battery's inner state for battery management system, an improved online parameters identification algorithm for equivalent circuit battery model is researched. To reduce the computation cost, the existing methods regarded the open circuit voltage over time as a constant value. However, when the sampling intervals are bigger, the estimation error of the battery state-of-charge calculated by the traditional method can be reach to 10% or more. Compared with the existing battery model parameter identification method, this study proposes a new online estimation method and which can estimate the battery open-circuit voltage in different sampling intervals with high accuracy. The results of the experiment, which uses Federal Urban Driving Schedule test to verify the parameters identification approach, show the proposed approach can accurately identify the model parameters within 1% maximum terminal voltage estimation error, and the state-of-charge error which calculated by the open circuit voltage estimates can be efficiently reduced to an accepted level.

A Precise FCC Estimation Algorithm Based on Recursive Least-Squares Identification of Li-Ion Batteries with Adaptive Forgetting Factor Tuning

Li-ion batteries are remarkable devices due to their high capability to store energy densely. The FCC (full charge capacity) estimation is essential for capturing the state of secondary battery. In this paper, precise FCC estimation is devised by estimation of internal parameter and SOC (state of charge). Comparted with the conventional identification techniques [1], the adaptive forgetting factor is more suitable for Li-ion battery. The open circuit voltage, OCV, is affected by SOC value. Therefore, the rate of change of OCV is not linear to time. In order to solve this problem, a heuristic adaptive forgetting factor is introduced based on terminal voltage and terminal current. To apply the system identification approach, the battery equivalent circuit model shown in Fig.1 is used. The subject of the system identification is OCV. OCV is physical quantity depending on SOC, and the relationship between OCV and SOC is given as Fig. 2. OCV-SOC curve has a significant role to achieve SOC estimation. The difference equation of u L is obtained by the equivalent circuit. Then, Equation (1) is obtained as observation function using the variables defined in Equation (2), and adding w (k) which is observation noise. T s is the sampling period. In equation (1), parameterθ regards as a unknown parameter, being estimated by using recursive least-squares identification. The value of R a, R b, C b, u OCV can be calculated by parameterθ with equation (3). SOC is obtained by referring the OCV-SOC curve. A heuristic forgetting factor λ(k) is defined by Equation (4). In this equation, G is gain, m uL is average variance of voltage u L preserving in buffer, and i avg is average value of current i. Estimation of OCV is performed using discharge patterns indicated in Fig.3. Table1 shows the average values of SOC estimation error. The average error is the smallest in the case of using the adaptive forgetting factor. Table2 shows the error dependent on temperature in the case of using the adaptive forgetting factor. SOC estimation is successful since the maximum value of average SOC estimation error is less than 0.05. Then, FCC is estimated with the estimated SOC. FCC is calculated by quotient of the value of current accumulation from time t0 to t1 and the change of estimated SOC value from t0 to t1. Ten percent discharges are executed from the 10 points of SOCs. The starting points of the discharge are from 0.97 to 0.92 by 0.05 intervals. The result of FCC estimation is shown Fig.4. In the case of 0.5A, the maximum value of average SOC estimation error is 0.049. Compared with the conventional techniques [2], the amount of calculation with proposed method is much less. The conventional technique [3] needs huge amount of data before estimation. In contrast, proposed method needs few data. This FCC estimation system pulls the maximum capability of secondary batteries with precise SOC estimation, and controls the batteries’ state by grasp of FCC. In addition, the amount of calculation and data needed preparing before estimation are less than conventional technique. Therefore, this proposed method can be implemented easily with inexpensive microcomputer. The experimentation has been executed in several conditions, and similar accurate results were obtained. [1] C. Fleischera, W. Waaga, H. Heyna, and D. U. Sauera, “On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models: Part 1. Requirements, critical review of methods and modeling,” J. Power Sources, vol. 260, no. 15, pp. 276-291, 2014. [2] T. Kim, Y. Wang, Z. Sahinoglu, T. Wada, S. Hara, W. Qiao, “A rayleigh quotient-based recursive total-least-squares online maximum capacity estimation for litium-ion batteries, ”IEEE trans. on energy conversion, vol. 30, no.3, pp. 842-850, 2015. [3] C. Hu, G. Jain, C. Schmidt, C. Strief, M. Sullivan, “Online estimation of lithium-ion battery capacity using sparse Bayesian learning, ” J. Power Sources, 289, pp. 105-113, 2015 Figure 1

Quantitative Analysis of Time-Domain Supported Electrochemical Impedance Spectroscopy Data of Li-Ion Batteries: Reliable Activation Energy Determination at Low Frequencies

Physico-chemical processes in batteries are taking place on a broad time scale from fractions of seconds to the order of days [1]. Thus, for an accurate characterization of transport and mobility processes in batteries using electrochemical impedance spectroscopy (EIS), a large frequency range of up to ten decades must be covered. This implies measurement durations on the order of days for low frequency measurements, yielding the risk of distorting electrochemical instabilities in the battery and a considerable change of its state of charge (SOC) due to the probing ac current excitation. It is shown that the SOC change is frequency dependent and with 10-15% of the nominal battery capacity for the sub-millihertz range hardly a small perturbation. Nevertheless, these obstacles can be mitigated by the time domain measurement (TDM) technique [2-4]. TDM is limited to impedance measurements at low frequencies, with a small and frequency-independent SOC change. The combination of TDM and EIS, called time-domain supported electrochemical impedance spectroscopy (TD-EIS), opens up the possibility for a time-efficient implementation of impedance spectroscopy over a large frequency range down to microhertz frequencies [5]. In this work, TD-EIS at varying temperatures in combination with data fitting using an electrical equivalent circuit battery model, is used for the high-accuracy quantification of low-frequency mobility parameters in lithium-ion batteries. It is experimentally demonstrated, for the first time, that the phase of the impedance measurements converges in the sub-millihertz range, which permits a reliable quantification of diffusion kinetics. Moreover, it is shown that with TD-EIS time savings of up to 80% compared to the standard EIS measurement are feasible. From the electrical equivalent circuit battery model fit, an accurate estimate of charge transfer resistance and, in particular, also solid-state diffusion rate are obtained. Both processes follow an Arrhenius law, allowing the determination of activation energies with small variance. The results for the charge transfer process and for the solid-state diffusion process are within the range of literature values measured for similar systems. This work has been published in JECS [6].

Battery State-of-Power Peak Current Calculation and Verification Using an Asymmetric Parameter Equivalent Circuit Model

In this paper, a higher fidelity battery equivalent circuit model incorporating asymmetric parameter values is presented for use with battery state estimation (BSE) algorithm development; particular focus is given to state-of-power (SOP) or peak power availability reporting. A practical optimization-based method is presented for model parameterization fitting. Two novel model-based SOP algorithms are proposed to improve voltage-limit-based power output accuracy in larger time intervals. The first approach considers first-order extrapolation of resistor values and open-circuit voltage (OCV) based on the instantaneous equivalent circuit model parameters of the cell. The second proposed approach, which is referred to as multistep model predictive iterative (MMPI) method, incorporates the cell model in a model predictive fashion. Finally, a SOP verification methodology is presented that incorporates drive cycle data to realistically excite the battery model. Simulation results compare the proposed SOP algorithms to conventional approaches, where it is shown that higher accuracy can be achieved for larger time horizons.

Design and use of multisine signals for Li-ion battery equivalent circuit modelling. Part 1: Signal design

The Pulse Power Current (PPC) profile is often the signal of choice for obtaining the parameters of a Lithium-ion (Li-ion) battery Equivalent Circuit Model (ECM). Subsequently, a drive-cycle current profile is used as a validation signal. Such a profile, in contrast to a PPC, is more dynamic in both the amplitude and frequency bandwidth. Modelling errors can occur when using PPC data for parametrisation since the model is optimised over a narrower bandwidth than the validation profile. A signal more representative of a drive-cycle, while maintaining a degree of generality, is needed to reduce such modelling errors.In Part 1 of this 2-part paper a signal design technique defined as a pulse-multisine is presented. This superimposes a signal known as a multisine to a discharge, rest and charge base signal to achieve a profile more dynamic in amplitude and frequency bandwidth, and thus more similar to a drive-cycle. The signal improves modelling accuracy and reduces the experimentation time, per state-of-charge (SoC) and temperature, to several minutes compared to several hours for an PPC experiment.

Robust Adaptive Sliding-Mode Observer Using RBF Neural Network for Lithium-Ion Battery State of Charge Estimation in Electric Vehicles

This paper presents a robust sliding-mode observer (RSMO) for state-of-charge (SOC) estimation of a lithium-polymer battery (LiPB) in electric vehicles (EVs). A radial basis function (RBF) neural network (NN) is employed to adaptively learn an upper bound of system uncertainty. The switching gain of the RSMO is adjusted based on the learned upper bound to achieve asymptotic error convergence of the SOC estimation. A battery equivalent circuit model (BECM) is constructed for battery modeling, and its BECM is identified in real time by using a forgetting-factor recursive least squares (FFRLS) algorithm. The experiments under the discharge current profiles based on EV driving cycles are conducted on the LiPB to validate the effectiveness and accuracy of the proposed framework for the SOC estimation.

Estimation method of state-of-charge for lithium-ion battery used in hybrid electric vehicles based on variable structure extended kalman filter

Since the main power source of hybrid electric vehicle(HEV) is supplied by the power battery, the predicted performance of power battery, especially the state-of-charge(SOC) estimation has attracted great attention in the area of HEV. However, the value of SOC estimation could not be greatly precise so that the running performance of HEV is greatly affected. A variable structure extended kalman filter(VSEKF)-based estimation method, which could be used to analyze the SOC of lithium-ion battery in the fixed driving condition, is presented. First, the general lower-order battery equivalent circuit model(GLM), which includes column accumulation model, open circuit voltage model and the SOC output model, is established, and the off-line and online model parameters are calculated with hybrid pulse power characteristics(HPPC) test data. Next, a VSEKF estimation method of SOC, which integrates the ampere-hour(Ah) integration method and the extended Kalman filter(EKF) method, is executed with different adaptive weighting coefficients, which are determined according to the different values of open-circuit voltage obtained in the corresponding charging or discharging processes. According to the experimental analysis, the faster convergence speed and more accurate simulating results could be obtained using the VSEKF method in the running performance of HEV. The error rate of SOC estimation with the VSEKF method is focused in the range of 5% to 10% comparing with the range of 20% to 30% using the EKF method and the Ah integration method. In Summary, the accuracy of the SOC estimation in the lithium-ion battery cell and the pack of lithium-ion battery system, which is obtained utilizing the VSEKF method has been significantly improved comparing with the Ah integration method and the EKF method. The VSEKF method utilizing in the SOC estimation in the lithium-ion pack of HEV can be widely used in practical driving conditions.

A novel multi-model probability battery state of charge estimation approach for electric vehicles using H-infinity algorithm

Due to the strong nonlinearity and complex time-variant property of batteries, the existing state of charge (SOC) estimation approaches based on a single equivalent circuit model (ECM) cannot provide the accurate SOC for the entire discharging period. This paper aims to present a novel SOC estimation approach based on a multiple ECMs fusion method for improving the practical application performance. In the proposed approach, three battery ECMs, namely the Thevenin model, the double polarization model and the 3rd order RC model, are selected to describe the dynamic voltage of lithium-ion batteries and the genetic algorithm is then used to determine the model parameters. The linear matrix inequality-based H-infinity technique is employed to estimate the SOC from the three models and the Bayes theorem-based probability method is employed to determine the optimal weights for synthesizing the SOCs estimated from the three models. Two types of lithium-ion batteries are used to verify the feasibility and robustness of the proposed approach. The results indicate that the proposed approach can improve the accuracy and reliability of the SOC estimation against uncertain battery materials and inaccurate initial states.

Estimating the State of Charge of Lithium-ion Battery based on Sliding Mode Observer

Battery management system (BMS) requires an accurate prediction of state of charge (SOC) of electric vehicles (EVs). In this paper, a first-order RC network equivalent circuit battery model with the hysteresis characteristic of Lithium-ion battery is built up. The parameters of battery equivalent circuit model (BECM) is identified. And then, we design a sliding mode observer (SMO) to estimate SOC of batteries in EVs. The robustness and observability of the SMO of SOC estimation are proved. Matlab/Simulink and AMESim co-simulation method is adopted to evaluate the performance of the presented algorithm. The simulation results show that the SOC estimation error is less than 3%.

Quantitative Analysis of Time-Domain Supported Electrochemical Impedance Spectroscopy Data of Li-Ion Batteries: Reliable Activation Energy Determination at Low Frequencies

For an accurate characterization of transport and mobility processes in batteries using electrochemical impedance spectroscopy (EIS), a large frequency range of up to ten decades must be covered. It is experimentally demonstrated, for the first time, that the phase of the impedance measurements converges in the sub-millihertz range, which permits a reliable quantification of diffusion kinetics. To avoid a considerable change of the state of charge (SOC) of the battery and to mitigate the very long measurement times caused by standard EIS, a combination of EIS and time domain measurements, the time-domain supported electrochemical impedance spectroscopy (TD-EIS), is employed. To ensure an utmost comparability and reproducibility of the results with minimum influence of the cell fabrication, the method is demonstrated using three equivalent, industrially manufactured lithium-ion pouch cells at varying temperatures. The obtained impedance data were fitted by an electrical equivalent circuit battery model for an accurate estimate of charge transfer resistance and, in particular, also solid-state diffusion rate. Both processes follow an Arrhenius law, allowing the determination of activation energies with small variance. The obtained results are within the range of literature values measured for similar systems. The relevance of very low frequency impedance data for accurate fitting of mobility parameters in batteries is discussed.

On-line optimization of battery open circuit voltage for improved state-of-charge and state-of-health estimation

A battery management system (BMS) ensures performance, safety and longevity of a battery energy storage system in an embedded environment. One important task for a BMS is to estimate the state of charge (SoC) and state of health (SoH) of a battery. The correlation between battery open circuit voltage (OCV) and SoC is an important reference for state estimation. The OCV-SoC correlation changes with respect to battery degradation. To improve the accuracy of state estimation, it is important to have the OCV-SoC correlation updated periodically.This work presents a solution by proposing a novel SoH(SoC) correlation as part of the battery equivalent circuit model (ECM). On-line optimization of SoH(SoC) correlation implicitly optimizes the OCV(SoC) correlation, as well as the capacity of a battery. An associated state and parameter dual estimator is proposed incorporating an Extended Kalman Filter (EKF) as a state observer, Recursive Least Square (RLS) algorithm as an internal resistance identifier, and Parameter Varying Approach as the SoH(SoC) correlation identifier. Battery experiment and simulation results validate that updating the SoH–SoC correlation effectively tracks battery SoH on-line. Furthermore, it implicitly updates OCV(SoC) function, further improving SoC estimation accuracy by 0.5%∼3%.

Parameters Identification and Simulation of Equivalent Circuit Model of Lead-Acid Battery

As a complex system, lead-acid batteries are affected by a number of factors, most of the lead-acid battery equivalent circuit models contain a large number of parameters, and the validity and accuracy of the models have a great relationship with the values of these parameters. Therefore, the parameter identification is a very important job of the modeling work. In this paper, we use the 7-HK-182 lead-acid battery for the study, doing charging and discharging experiments of this lead-acid battery, establish an equivalent circuit model, and identifying the parameters of this model, at last, through the simulation, we determine the accuracy of the parameters identification of the equivalent circuit model.

Cost-Optimal Charging of Plug-In Hybrid Electric Vehicles Under Time-Varying Electricity Price Signals

This paper develops a convex quadratic programming (QP) framework for the charge pattern optimization of plug-in hybrid electric vehicles (PHEVs) under time-varying electricity price signals. The work is motivated by the need for a computationally efficient PHEV charging model in the bidirectional vehicle-to-grid (V2G) integration studies, accounting for the hybrid powertrain dynamics and battery energy losses of the PHEVs. We adopt a previously developed PHEV power management system and construct a simplified model for the convex optimization problem. We use an equivalent circuit battery model to compute battery energy losses during grid charging and discharging. We then derive the total fuel and electricity cost of the PHEV as a quadratic function of battery state of charge and use a standard QP solver to minimize it for a few sample trips obtained from the National Household Travel Survey data set. Using a quad-core computer, the daily PHEV charging trajectory with 5-min time resolution can be optimized in less than tenth of a second. Through several examples, we show the application of the proposed method in various V2G-related problems, such as obtaining the aggregate load patterns of PHEVs, analyzing the potential impacts of large-scale bidirectional V2G integration, benchmarking the fuel economy of PHEVs, and determining the sensitivity of V2G load to abrupt price variations.