Battery Management System Applications Research Articles

Enhanced multi-constraint dung beetle optimization-kernel extreme learning machine for lithium-ion battery state of health estimation with adaptive enhancement ability

Accurately estimating the state of health (SOH) of lithium batteries is a critical and challenging task in battery management systems. Data-driven models are widely used for SOH estimation but still suffer from the difficulty of balancing speed, accuracy, and adaptability. Therefore, this study constructs the dung beetle optimization algorithm to optimize the kernel extreme learning machine model. This paper addresses the issues of long iteration time and mismatches in kernel function mapping in data-driven models. To improve the model's generality, an adaptive learning kernel function is designed to complement the polynomial kernel function and form a joint function. This joint function is then introduced into a single implicit-layer extreme learning machine, which achieves fast speed and strong adaptive capability. To enhance the algorithmic parameter search capability, the optimal Latin hypercube idea, and the Osprey algorithm's global exploration strategy are introduced, which effectively improves the algorithm's global search capability. Additionally, it successfully regulated the positional update through the design of the logarithmic weighting factor, which improved the local search and convergence capabilities of the algorithm. The experiment validates the effectiveness and rationality of the proposed model for advancing battery management system applications.

Data selection framework for battery state of health related parameter estimation under system uncertainties

Data selection is a practical technique for improving parameter estimation accuracy through the strategic selection of information-rich data for use in the estimation algorithm. Traditional selection criteria have been either heuristic or sensitivity-based, without consideration of uncertainties in measurement, model, or parameter. In this paper, we propose an uncertainty-aware data selection framework that selects data segments based on the potential of the ingrained data structures to mitigate the influence of system uncertainties on the estimation result. The framework comprises two components: the data quality rating and data selection algorithm. The data quality rating is a metric for evaluating the uncertainty-propagating data structures of a data segment, and the data selection algorithm automatically integrates the data selection into the estimation procedure. Furthermore, a novel adaptive approximation of model/measurement uncertainty is derived and implemented in the data quality rating formula to enhance performance in the presence of time-varying sensor bias/noise and unmodeled system dynamics. The framework is validated through an advanced battery management system application, where two lithium-ion battery health-related electrochemical parameters are separately estimated under random drive-cycle input data to emulate battery state of health monitoring for an electric vehicle. We show that the drive-cycle data, which are frequently used for battery state of health estimation as the only available data during battery operation, may not provide accurate estimation results due to the existence of large portions of low-quality data (low sensitivity and high uncertainty). By extracting the high-quality data segments, the data selection framework reduced experimental estimation errors by one order of magnitude when compared with the conventional approach of estimating without data selection.

A NARX network optimized with an adaptive weighted square-root cubature Kalman filter for the dynamic state of charge estimation of lithium-ion batteries

Due to the high nonlinearities and unstable working conditions, accurately estimating the state of charge (SOC) by the battery management system (BMS) is a major challenge in ensuring the safety and reliability of lithium-ion batteries in electric vehicles. This paper presents a deep learning network, a nonlinear autoregressive model with exogenous inputs (NARX) network with a closed-loop architecture and transfer learning mechanism, which is optimized using a proposed adaptive weighted square-root cubature Kalman filter (AWSCKF) with a moving sliding window and an adaptive weighing coefficient for SOC estimation of lithium-ion batteries. The proposed AWSCKF method is established through square-root and cubature updates to optimize the statistical value of the state estimate, error covariance, and measurement noise covariance matrices, with the ability to incorporate high nonlinearities to filter out the noise, stabilize, and optimize the final SOC. To evaluate the effectiveness of the optimized NARX network and verify the proposed AWSCKF method, battery tests are carried out using a lithium cobalt oxide battery at various charge-discharge rates and a lithium nickel cobalt manganese oxide battery at temperatures of 0 and 45 °C under five complex working conditions. The SOC accuracy of lithium-ion batteries is enhanced by the hybrid method estimation process, which is based on sensitivity analysis and adaptation to various working conditions. The comprehensive results show that the proposed NARX-AWSCKF model achieves the overall best mean absolute error, root mean square error, and mean absolute percentage error values of 0.07293%, 0.0912%, and 0.40356%, respectively, under various complex conditions. By effectively utilizing battery domain knowledge for real-world BMS applications, the proposed model outperforms other existing methods in terms of high effectiveness, robustness, and potential to boost the NARX performance.

Robust adaptive sliding mode observer for core temperature and state of charge monitoring of Li-ion battery: A simulation study

State of charge (SOC) and temperature monitoring of Li-ion batteries (LIBs) via battery management system (BMS) is crucial to ensure proper and secure performance of LIBs. Monitoring methods based on electrochemical models are highly accurate, which stems from their phenomenological nature; however, such multi-dimensional and rigorous models are computationally time-consuming and elaborate to implement. Consequently, a relatively accurate but more straight-forward estimation method with fast computational capabilities is needed in real-life BMS applications. In this work, an equivalent circuit model (ECM) together with a lumped thermal model has been considered as design model for an online adaptive sliding mode observer. This observer uses measurement of battery terminal voltage and surface temperature in order to estimate SOC and core temperature, both of which play decisive role in BMS applications. The proposed observer performance has been validated in constant current and urban dynamometer driving schedule (UDDS) load profile experiments, where inspection of results overwhelmingly indicates its utmost stability as well as robust performance in comparison with commonly used observers.

Enhanced multi-state estimation methods for lithium-ion batteries considering temperature uncertainties

Due to their high energy density and minimal emissions, lithium-ion batteries are frequently employed in electric vehicles (EVs). Accurate estimation of the micro-parameters, state of charge (SOC), and state of health (SOH) are a few primary monitoring functions of the battery management system (BMS) to increase the battery's efficiency and safety under various operating conditions. This paper proposes a SOC and SOH co-estimation method by adopting an ensemble empirical mode decomposition method with adaptive noise and an autoencoder (EEMDA) to extract, decompose, and reconstruct the full-scale charging voltage and current data for a dual extended Kalman filter (DEKF) with multi-parameter and time-scale updates for accurate estimation based on a variable forgetting factor limited memory recursive least squares (VFF-LMRLS) method. The VFF-LMRLS method is used to solve the data saturation phenomenon and identify the battery's characteristic micro-parameters based on a proposed dynamic migration second-order resistor-capacitor equivalent circuit model under different operating states. Battery tests are conducted at temperatures ranging from −10 to 50 °C under complex working conditions. Using the VFF-LMRLS method, the effects of different temperatures on the micro-parameters are discussed. The SOC and SOH results of the proposed EEMDA-DEKF method based on the dynamic migration battery model show that the mean absolute error and root mean square error metrics have the least values of 0.0233% and 0.0252%, which signify an optimal performance improvement of 93.26% and 93.66%, respectively, compared to the conventional DEKF method. Based on the experimental results and analyses, the proposed method has a high degree of accuracy and robustness, which makes it feasible for battery monitoring and prognostic BMS applications.

A Review of Lithium-Ion Battery Capacity Estimation Methods for Onboard Battery Management Systems: Recent Progress and Perspectives

With the widespread use of Lithium-ion (Li-ion) batteries in Electric Vehicles (EVs), Hybrid EVs and Renewable Energy Systems (RESs), much attention has been given to Battery Management System (BMSs). By monitoring the terminal voltage, current and temperature, BMS can evaluate the status of the Li-ion batteries and manage the operation of cells in a battery pack, which is fundamental for the high efficiency operation of EVs and smart grids. Battery capacity estimation is one of the key functions in the BMS, and battery capacity indicates the maximum storage capability of a battery which is essential for the battery State-of-Charge (SOC) estimation and lifespan management. This paper mainly focusses on a review of capacity estimation methods for BMS in EVs and RES and provides practical and feasible advice for capacity estimation with onboard BMSs. In this work, the mechanisms of Li-ion batteries capacity degradation are analyzed first, and then the recent processes for capacity estimation in BMSs are reviewed, including the direct measurement method, analysis-based method, SOC-based method and data-driven method. After a comprehensive review and comparison, the future prospective of onboard capacity estimation is also discussed. This paper aims to help design and choose a suitable capacity estimation method for BMS application, which can benefit the lifespan management of Li-ion batteries in EVs and RESs.

Remaining useful cycle life prediction of lithium-ion battery based on TS fuzzy model

Accurately predicting the remaining useful cycle life of a lithium-ion battery is essential for health management of battery systems. Aiming at the time-varying and nonlinear problems of lithium-ion batteries, a remaining useful cycle life estimation method based on Takagi-Sugeno fuzzy model is proposed, which not only reduces the amount of data calculation, but also reduces massive data and has high accuracy. First, collect the rate of change of working voltage in the charging process, and analyze the relationship between the position of voltage rate curve and the number of cycles. Second, in order to reduce the amount of historical data, the interval with obvious mapping relationship is selected, and the recursive least square method is used to fit the curve off-line, which reduces the amount of data calculation and is easy to achieve in battery management system engineering. And then, the Takagi-Sugeno fuzzy model is applied to establish the remaining useful cycle life method based on Takagi-Sugeno fuzzy model. Finally, battery management system application shows that the proposed method can achieve high prediction accuracy and also provides a new perspective for remaining useful cycle life prediction.

An optimized relevant long short-term memory-squared gain extended Kalman filter for the state of charge estimation of lithium-ion batteries

Accurate state of charge (SOC) estimation of lithium-ion batteries by the battery management system (BMS) plays a prominent role in ensuring their reliability, safe operation, and acceptable durability in smart devices, electric vehicles, etc. In this paper, the effect of the training and testing working conditions on the accuracy of the SOC using a long short-term memory (LSTM) network is studied through transfer learning. Then, a relevant attention mechanism is introduced as a data optimizer for faster training of the LSTM network to establish a relevant LSTM (RLSTM). Finally, the SOCs estimated by the RLSTM are independently input with the working current to an extended Kalman filter (EKF) and a proposed squared gain EKF (SGEKF) method to iteratively denoise and optimize the accuracy of the final SOC under the three complex working conditions. The results show that the SOC estimation accuracy is influenced by the training and testing working conditions using the LSTM network, which provides a technique for accurate SOC estimation. Also, the established RLSTM network is computationally efficient for accurate SOC estimation. Moreover, the proposed hybrid RLSTM-SGEKF model has an overall maximum mean absolute error, mean squared error, root mean squared error, and mean absolute percentage error values of 0.35299%, 0.0017448%, 0.41765%, and 2.34403%, respectively, under the three complex working conditions. The proposed hybrid RLSTM-SGEKF model is optimal, robust, and computationally efficient for accurate SOC estimation of lithium-ion batteries for real-time BMS applications.

Differential evolution based regression algorithm for mathematical representation of electrical parameters in lithium-ion battery model

Accurate equivalent electric circuit models of a lithium-ion battery, generally consisting of lumped electrical parameters, are of utmost importance for implementing various algorithms in Battery Management System (BMS). The low-cost Electronic Control Unit for BMS application prompts for an accurate representation of these parameters with a reduced memory footprint is significant. This prompted the representation of SoC dependant parameters as polynomial, Gaussian, sum of sine and exponential equations through regression algorithms instead of a lookup table. This article proposes Differential Evolution (DE) based Regression algorithm to represent the experimentally pre-identified parameters as a function of SoC through the aforementioned equations. Based on the experimental test, data points representing the SoC dependency of battery parameters such as average open-circuit voltage, hysteresis, internal resistances, and capacitance have been obtained. These data points are subjected to a proposed algorithm to establish the mathematical relationship between the parameters and SoC. The flexibility of the algorithm has been verified by considering the aforesaid equations. The DE based regression algorithm's performance was compared with various other algorithms in terms of statistical parameters such as RMSE, Mean Average, and Variance. Based on the analysis of the obtained results for various algorithms, the equations developed by DE based regression algorithm have the best fit with experimental data for all the aforementioned equations. The analysis depicts that the eighth order polynomial equation fitted by the proposed algorithm is highly accurate. Various battery models have been validated with the experimental data based on the developed equations for all parameters.

A comprehensive equivalent circuit model for lithium-ion batteries, incorporating the effects of state of health, state of charge, and temperature on model parameters

The equivalent circuit model (ECM) is a battery model often used in the battery management system (BMS) to monitor and control lithium-ion batteries (LIBs). The accuracy and complexity of the ECM, hence, are very important. State of charge (SOC) and temperature are known to affect the parameters of the ECM and have been integrated into the model effectively. However, the effect of the state of health (SOH) on these parameters has not been widely investigated. Without a good understanding of the effect of SOH on ECM parameters, parameter identification would have to be done manually through calibration, which is inefficient. In this work, experiments were performed to investigate the effect of SOH on Thevenin ECM parameters, in addition to the effect of SOC and temperature. The results indicated that with decreasing SOH, the ohmic resistance and the polarization resistance increase while the polarization capacitance decreases. An empirical model was also proposed to represent the effect of SOH, SOC, and temperature on the ECM parameters. The model was then validated experimentally, yielding good results, and found to improve the accuracy of the Thevenin model significantly. With low complexity and high accuracy, this model can be easily integrated into real-world BMS applications.

Python‐based scikit‐learn machine learning models for thermal and electrical performance prediction of high‐capacity lithium‐ion battery

With the increasing popularity of electric vehicles (EVs), the demands for rechargeable and high-performance batteries like lithium-ion (Li-ion) batteries have soared. Li-ion battery systems require the use of a battery management system (BMS) to perform safely and efficiently. Accurate and reliable battery modeling is important for the BMS to function properly. Currently, many BMS applications use the equivalent circuit model due to its simplicity. However, with the development of a cloud BMS, machine learning battery models can be utilized, which can potentially improve the accuracy and reliability of the BMS. This work investigates the performance of four different machine learning models used to predict the thermal (temperature) and electrical (voltage) behaviors of Li-ion battery cells. A prismatic Li-ion battery cell with a capacity of 25 Ah was cycled under a constant current profile at three different ambient temperatures, and the surface temperature and voltage of the battery were measured. The four machine learning regression models—linear regression, k-nearest neighbors, random forest, and decision tree—were developed using the scikit-learn library in Python and validated with experimental data. The results of their performance were reported and compared using the R2 metric. The decision tree-based model, with an R2 score of 0.99, was determined to be the best model in this case study.

Comprehensive Review on Smart Techniques for Estimation of State of Health for Battery Management System Application

Electric Vehicles (EV) and Hybrid EV (HEV) use Lithium (Li) ion battery packs to drive them. These battery packs possess high specific density and low discharge rates. However, some of the limitations of such Li ion batteries are sensitivity to high temperature and health degradation over long usage. The Battery Management System (BMS) protects the battery against overvoltage, overcurrent etc., and monitors the State of Charge (SOC) and the State of Health (SOH). SOH is a complex phenomenon dealing with the effects related to aging of the battery such as the increase in the internal resistance and decrease in the capacity due to unwanted side reactions. The battery life can be extended by estimating the SOH accurately. In this paper, an extensive review on the effects of aging of the battery on the electrodes, effects of Solid Electrolyte Interface (SEI) deposition layer on the battery and the various techniques used for estimation of SOH are presented. This would enable prospective researchers to address the estimation of SOH with greater accuracy and reliability.

Comparative Study of Equivalent Circuit Models Performance in Four Common Lithium-Ion Batteries: LFP, NMC, LMO, NCA

Lithium-ion (Li-ion) batteries are an important component of energy storage systems used in various applications such as electric vehicles and portable electronics. There are many chemistries of Li-ion battery, but LFP, NMC, LMO, and NCA are four commonly used types. In order for the battery applications to operate safely and effectively, battery modeling is very important. The equivalent circuit model (ECM) is a battery model often used in the battery management system (BMS) to monitor and control Li-ion batteries. In this study, experiments were performed to investigate the performance of three different ECMs (1RC, 2RC, and 1RC with hysteresis) on four Li-ion battery chemistries (LFP, NMC, LMO, and NCA). The results indicated that all three models are usable for the four types of Li-ion chemistries, with low errors. It was also found that the ECMs tend to perform better in dynamic current profiles compared to non-dynamic ones. Overall, the best-performed model for LFP and NCA was the 1RC with hysteresis ECM, while the most suited model for NMC and LMO was the 1RC ECM. The results from this study showed that different ECMs would be suited for different Li-ion battery chemistries, which should be an important factor to be considered in real-world battery and BMS applications.

A Dynamic High-Order Equivalent Modeling of Lithium-Ion Batteries for the State-of-Charge Prediction Based on Reduced-Order Extended Kalman Filtering Algorithm

Detection of battery power has always been the core of the battery management system of electric vehicles, and the fast and accurate estimation of charged state can guarantee the safe operation of electric vehicles. The key to improving accurate state-of-charge estimation is an appropriate model establishment coupled with a suitable estimation algorithm. This research seeks to adopt and accomplish a lithium-ion battery state-of-charge estimation based on the Gaussian function to build up the open-circuit voltage algorithm. A reduced-order extended Kalman filtering algorithm is proposed with hybrid pulse power characterization parameter identification to estimate the battery characterization state-of-charge. The model’s parameters in different state-of-charge points are calculated through the lithium-ion battery’s charge and discharge process; the 2RC modeling correction method and Reduced-order extended Kalman filter method are used separately based on the High-order equivalent 2RC modeling. The Experimental results show that the above method can achieve state-of-charge estimation more accurately and conveniently, providing a certain reference value for the rational management and distribution of power lithium-ion batteries. The maximum error of state-of-charge estimation based on the established high-order equivalent 2RC model using the Reduced-order extended Kalman filtering algorithm is less than 1.85%. The REKF algorithm achieved a maximum voltage error of 0.0409V and an average error of 0.0299V and therefore can satisfy the accuracy of the battery management system application needs. Keywords: Lithium-ion battery; state-of-charge; high-order equivalent 2RC modeling; open-circuit voltage; parameter identification; reduced-order extended Kalman filtering algorithm DOI: 10.7176/JETP/11-3-03 Publication date: June 30 th 2021

An improved single-particle model with electrolyte dynamics for high current applications of lithium-ion cells

In this work, an isothermal, reduced-order polynomial-based model is proposed for lithium-ion cells. The correction incorporated into the single-particle model considers the effect of electrolyte dynamics leading to improved model predictions at high current applications without adding any significant computational complexity. The model includes the spatial distribution of the electrode and electrolyte potentials and the electrolyte lithium concentration on the resulting cell voltage. A novel approach to account for the spatially varying overpotential and open-circuit potential is proposed. A linear system of differential-algebraic equations is obtained in the state variables and the cell voltage is computed using a non-linear expression in these states. The resulting linear state-space system makes the model easily implementable for state-estimation algorithms in battery management system applications. Additionally, a semi-analytical model is incorporated for the diffusion of lithium in electrodes and a criterion for truncating the infinite-series solution is proposed for achieving a balance between accuracy and complexity for cells subjected to fluctuating currents. The proposed model results in a decrease in error for cell voltage prediction by a factor of five when compared with existing enhanced single-particle models.

A review on state of health estimations and remaining useful life prognostics of lithium-ion batteries

Lithium-ion batteries have been generally used in industrial applications. In order to ensure the safety of the power system and reduce the operation cost, it is particularly important to accurately and timely estimate the state of health (SOH) and predict the remaining useful life (RUL) of lithium-ion batteries. With the development of intelligent tools such as artificial intelligence, big data analysis and the Internet of Things, the methods of battery health assessment have been gradually diversified. Here, we have compiled four publicly available battery datasets. The SOH estimations and RUL prognostics of lithium-ion batteries are reviewed by analyzing the research status. To this end, after studying different scientific and technical literatures, the respective methods are divided into specific groups, and the advantages and limitations of the battery management system application are discussed. At the end, the future development trend and research challenges are analyzed. All key insights in this review will hopefully drive the development of battery health estimation and life prediction techniques.

Real-Time Under-Load Electrochemical Impedance Spectroscopy (EIS) Analysis and Modeling

All batteries degrade, but the challenge comes in quantifying that degradation and ultimately predicting a battery's failure and/or end-of-life. Battery health and monitoring have become more imperative with larger deployment of lithium batteries in electric vehicle (EV) and energy storage system (ESS) applications. Research shows a strong correlation between battery degradation and AC impedance measured using electrochemical impedance spectroscopy (EIS). This indicates that AC impedance can be used as a proxy for battery health. Additional information, like a battery's internal temperature can also be extracted from EIS measurements. As such, there is a strong push to measure AC impedance of a battery in field diagnostic applications. However, EIS is typically performed at rest under very stable environmental conditions. This traditional method of interpreting EIS must be modified to account for changing environmental conditions and changing current loads like those seen in EV and ESS applications. This paper explores the prospect of using EIS in a real-time battery management system (BMS) with the primary focus on determining the limits for interpreting EIS under loaded current conditions. An experiment is conducted to evaluate using EIS measurements taken on a loaded battery for the purpose of temperature estimation.A set of experiments were conducted where EIS was performed on Samsung 18650 Nickel Manganese Cobalt (NMC) cells while the cell was subject to loaded conditions. These experiments consisted of load currents ranging from charging rates (C-rate) between C/5 to 2C, and discharging rates (D-rate) between D/5 to 2D. Test were conducted at temperatures in the range of 5°C to 35°C. Closer inspection of Figure 1 shows EIS spectra diverging for charging conditions at lower frequencies. This is believed to be caused by a drift in the battery’s SOC. During charging, lower frequencies in AC impedance tend to have lower magnitude. Conversely, higher AC impedance magnitude is observed during discharging. The EIS frequency at which the loaded impedance deviates from the unloaded impedance by >10% is determined. The curve in Figure 2 represents the lowest EIS frequency at which under load EIS spectra is deemed usable, meaning that the shaded region below the curve represents the unusable portion of the EIS spectra. Moreover, this relationship serves as groundwork upon which to correct for EIS under loaded conditions. It is believed that the relationship of frequency limit as a function of load current shown in Figure 2 is slightly skewed by battery heating as an artifact of the test procedure. As a result, this experiment will be repeated prior to the final paper to gather data that accounts for these heating effects. A method to correct for shifts in an under-load EIS spectra will also be presented in the final paper.The prospect of using an under-load EIS spectra for internal temperature prediction is also demonstrated on a lab scale. In this experiment, the Samsung cell was soaked in a thermal chamber at constant temperature for several hours. A series of 3D discharge pulses are then applied to the battery for various durations. EIS is performed back-to-back during the current pulses (i.e., under load) and during rest times. The EIS spectra are fed into a cell temperature estimation model based on a non-zero interrupt frequency (NZIF) method. Figure 3 shows how EIS spectra changes with temperature for both loaded and unloaded conditions. The details of the NZIF model are beyond the scope of this paper. Thermistors are placed on the surface of the battery to measure a reference temperature. The results of the NZIF-predicted internal temperature are contrasted with measured thermistor battery surface temperatures, and those results are shown in Figure 4. These results indicate that NZIF-predicted internal temperature rises and falls during discharge and rest events, consistent with expected temperature rise and thermistor-measured battery surface temperature.Preliminary analysis suggests that constant current loads only slightly skew no-load EIS measurements, and that most of the EIS spectra taken under load is still usable. Furthermore, the usable portion of an EIS spectra can be determined by an EIS frequency vs load current relationship. This paper demonstrated that EIS can be used for internal temperature prediction while the battery is subject to a loaded condition, which is potentially useful to improve safety and performance of battery packs in field applications. In future work, more EIS measurements will be taken under different loaded conditions to improve NZIF predictions of internal temperature. Nevertheless, these early results are extremely promising for the use of EIS in real-time BMS applications. Figure 1

A Robust Online Parameter Identification Method for Lithium-Ion Battery Model Under Asynchronous Sampling and Noise Interference

Online identification of a battery model can capture the parameter variations in real time, thus, providing an accurate model under various conditions, such as a wide temperature range, different aging degree in electric vehicle application. However, the measurement noise and sampling asynchronization of voltage and current are usually inevitable in the battery management system (BMS), which can lead to a large identification error. In this article, the mechanism of sampling asynchronization and measurement noise is analyzed first, and then the identification sensitivity analyses on noise and sampling asynchronization are carried out. Simulation results indicate that even a small fluctuation as small as 5 mV or the sampling latency between voltage and current within 10 mS can cause relatively large identification errors, especially for polarization parameters. In order to guarantee the online identification accuracy and robustness in the BMS application, an improved robust recursive least-squares (RLS) algorithm with adaptive outlier boundary is proposed to eliminate the input outlier caused by sampling latency and suppress the effect of measurement noise utilizing the bias compensation method. The experimental results demonstrate that the proposed method can provide sufficient accuracy and robustness under noise interference and sampling latency in BMS application.

A robust approach to state of charge assessment based on moving horizon optimal estimation considering battery system uncertainty and aging condition

Accurate battery state information is essential for battery management system application and safety monitoring. However, it is a challenge task to obtain satisfied estimation results due to the uncertainties and inconsistencies of battery packs caused by aging. To solve this challenge, an optimization-based moving horizon estimation approach is presented in this paper for battery state and parameter online estimation. The dynamic battery parameters including open circuit voltage and internal resistance in equivalent circuit model are described by polynomial function of state of charge and input current for estimation algorithm design. And the intrinsic connection and difference between extended Kalman filter and moving horizon estimation algorithm are explicitly explained. Both of them are least square based estimation approach, and Kalman filter is a special form of moving horizon estimation, while moving horizon estimation relax Markov assumption compared with extended Kalman method. And then the optimization-based moving horizon estimation is designed for parameters and state of charge online assessment for battery dynamic system. To reduce computing time, the software framework CasADi is used for differential-algebraic calculation and nonlinear optimization. Three mismatch working conditions are studied for estimation performance validation, including mismatched initial guess values and battery dynamic characteristics difference caused by aging condition. The experimental results demonstrate that optimization-based moving horizon estimation performs better than Kalman filter-based approaches in terms of estimation precision, convergence time and robust. The proposed optimization-based moving horizon estimation is a promising approach for state of charge estimation in commercial battery management system applications.

An On-Board Model-Based Condition Monitoring for Lithium-Ion Batteries

A model-based condition monitoring for lithium-ion (Li-ion) batteries involves estimating critical model parameters (e.g., capacity and impedance) and operational states [e.g., state of charge (SOC) and state of health]. This is important to design high-performance and safety-critical battery systems. Moreover, the tuning parameters of the condition monitoring algorithms significantly influence the performance of the algorithms. This paper proposes a real-time model-based condition monitoring for Li-ion batteries based on a real-time second-order resistor–capacitor electrical circuit battery model. The proposed method consists of an extended Kalman filter based online parameter identification and a smooth variable structure filter based state estimation. The two filters are systematically integrated to cooperate with each other and named hybrid filter (HF). Furthermore, a proposed particle swarm optimization based tuning parameter optimization is employed to find the optimal tuning parameters of the HF. The proposed method is compared with the dual extended Kalman filter (DEKF) via simulations and validated by experiments using a low-priced microcontroller. The results show that the proposed method can effectively choose the tuning parameters and has less computational complexity and higher accuracy of the SOC and capacity estimation than those of the conventional DEKF. Therefore, the proposed HF can be suitable for use in real-time embedded battery management system applications.