Battery Equivalent Circuit Model Research Articles

A fusion algorithm of multidimensional element space mapping architecture for SOC estimation of lithium-ion batteries under dynamic operating conditions

Accurate estimation of the state of charge (SOC) is pivotal for ensuring the reliable operation of lithium-ion batteries in electric vehicles, particularly under complex real-world conditions. This paper introduces a novel SOC estimation method named Multidimensional Elemental Space Mapping Architecture (MESMA), which integrates the battery equivalent circuit model with a data-driven approach to tackle adaptability under intricate conditions and high-dimensional input data correlation. Initially, a least squares method incorporating a forgetting factor is employed to identify the battery circuit model parameters and analyze their correlation with SOC. Subsequently, a feature fusion algorithm is introduced to discern spatial variables highly correlated with SOC by leveraging both original voltage and current data and circuit model parameters as inputs to a Convolutional Neural Network (CNN) model, and an eight-input and one-output spatially mapped feature CNN model is established. Finally, the XGBoost model is harnessed for battery SOC estimation. The effectiveness and adaptability of MESMA are validated using experimental data from both public single condition and mixed condition datasets, including FUDS, Mixed-1, etc. The results unequivocally demonstrate that MESMA accurately estimates the SOC of lithium-ion batteries under varying operating conditions. Furthermore, it exhibits remarkable adaptability and stability across different temperatures, effectively capturing SOC trends.

Construction and Analysis of Battery Equivalent Circuit Model Considering Liquid Phase Lithium Ion Diffusion Under High-Rate Conditions

In order to obtain the internal state of lithium-ion battery quickly and accurately, the problem that the internal state of the battery is difficult to estimate quickly and accurately is solved. The discharge performance of lithium ion is affected by the electrode current during the charge and discharge process. This paper analyzes the key factors of the electrochemical model at high rate, considers the change of lithium ion concentration in the liquid phase of the battery, integrates the electrochemical mechanism and the equivalent circuit, and establishes a mechanism equivalent circuit model with more computational advantages through circuit elements. The equivalent circuit model can describe the physical characteristics of the lithium battery. Under high rate constant current and dynamic conditions, the model shows good electrical characteristics. Compared with the traditional empirical equivalent circuit model, the accuracy of the model is improved, and the state quantity is reduced by 15 compared with the electrochemical model. The model is of great significance in practical application.

A high-fidelity lithium-ion battery emulator for electric vehicle application

Lithium-ion (Li-ion) battery has played a key role for the development of electric vehicle (EV) at present, while the Li-ion batteries in the market come from different manufactures. Verifying the performance of the battery management system (BMS) for various battery chemistries is a complex undertaking. This paper proposes a high-fidelity Li-ion battery emulator for EV applications. The emulator utilizes a battery model parameterized by a series of performance tests and a special-designed hardware platform. A three-order battery equivalent circuit model (ECM) is selected to provide the voltage and current reference signal in the processor. Subsequently, the hardware generates the high voltage and current signal in accordance with the reference. To ensure the high accuracy of the battery ECM, a 37 Ah nickel manganese cobalt (NMC) battery was selected for testing under both charge and discharge conditions, as well as across a temperature range of − 30℃ to 45℃. The battery emulator is verified on charge and discharge mode for both accuracy and dynamic performance validations.

Understanding the Interplay of Battery and Flight Dynamics Using Coupled Battery and Flight Physics Simulations for Electric Aircraft

Electric aviation has been a major focus of research in recent years as the aviation industry has seen significant growth in electric aircraft development. Most of the current literature related to electric aircraft modeling focuses on aircraft design and optimization with less focus given to battery analysis. Many studies utilize battery simplifications such as linear voltage profiles1 or the use of equivalent circuit models2. Similarly, in the emerging field of electric vertical takeoff and landing (eVTOL) aircraft, battery analysis is often reduced to considering just weight and empirical power parameters, failing to capture physical and electrochemical battery behavior and its effect on battery performance characteristics3. These simplifications can often lead to inaccurate battery state estimations and performance prediction. Moreover, the battery packs used for both electric conventional take-off and landing (eCTOL) aircraft and eVTOLs see unique operating requirements that are often significantly more demanding than those seen in electric vehicles (EVs)4. This suggests the need to analyze aircraft battery pack performance limitations in greater detail. However, only a few such studies have been reported in the literature5-6.In this work, we perform coupled simulation studies of longitudinal flight dynamics and physics-based battery dynamics. For modeling battery dynamics, we use the well-known single particle model7. This coupling enables more reliable estimation of battery states and can better inform battery pack design for electric aircraft. The simulations are performed to understand the interplay between battery cell dynamics governed by its design parameters and parameters associated with fixed-wing flight dynamics, such as cruise altitude, flight path angle, and velocity. Additionally, the simulations show how varying these parameters and operating temperature effects the range and endurance of electric aircraft which can be used to determine the optimal aircraft operating parameters for a desired mission profile. Results from this simulation study are compared against an equivalent circuit battery model to highlight the importance of detailed battery analysis in electric aviation. This work will be extended to develop similar coupled physics-based battery models with the state-of-the-art aircraft configurations emerging in the eVTOL field.References M. Kaptsov and L. Rodrigues, Journal of Guidance, Control, and Dynamics, 41, 288 (2018).N. Biju and H. Fang, Applied Energy, 339, 120905 (2023).L. Kiesewetter, K. H. Shakib, P. Singh, M. Rahman, B. Khandelwal, S. Kumar and K. Shah, Progress in Aerospace Sciences, 142, 100949 (2023).X.-G. Yang, T. Liu, S. Ge, E. Rountree and C.-Y. Wang, Joule, 5, 1644 (2021).A. Ayyaswamy, B. S. Vishnugopi and P. P. Mukherjee, Joule, 7, 2016 (2023).M. Wang, S. Kolluri, K. Shah, V. R. Subramanian and M. Mesbahi, IEEE Transactions on Aerospace and Electronic Systems, 59, 1084 (2022).S. Santhanagopalan, Q. Guo, P. Ramadass and R. E. White, Journal of power sources, 156, 620 (2006).

Adaptive Neural Network-Based Event-Triggered SOC Observer With Application to a Stochastic Battery Model.

Accurate state of charge (SOC) is crucial to achieving safe, reliable, and efficient use of batteries. This article proposes an adaptive neural network (NN)-based event-triggered observer to estimate SOC. First, a stochastic battery equivalent circuit model (ECM) is established, where an adaptive NN is employed to approximate the unknown nonlinear part. The learning process of network weight is conducted online to observe the variations of model parameters and avoid time-consuming processes for parameter extraction. Besides, for the purpose of saving computational cost, an event-triggered mechanism (ETM) is employed in the weight updating law, which means the weights only update when it is necessary. Then, an adaptive radial basis function (RBF) NN-based SOC observer is designed, and its stability is proven by the Lyapunov theory. Moreover, the strictly positive lower bound of interevent time is derived, and undesirable Zeno behavior can be excluded. Finally, the accuracy and robustness of the proposed observer are evaluated by experiments and simulations. Results show that the proposed method can estimate SOC accurately in the presence of initial deviation and sensor noises.

Comparative analysis of equivalent circuit battery models for electric vehicle battery management systems

Lithium-ion batteries need to be controlled by a Battery Management System (BMS) to operate safely and efficiently. BMS controls parameters, such as current, voltage, temperature, state of charge (SoC),state of health (SoH), state of power (SoP) and etc. The battery models and several prediction algorithms that the BMS uses to carry out these checks are essential to the system's performance. Therefore, the battery model is crucial to the BMS. This model is used to optimize the performance, capacity, lifetime and safety of the battery. Using the accurate battery model for BMS and electric vehicles can improve energy efficiency, extend battery life and reduce safety risks. Therefore, it is important that the model can accurately reflect the battery behavior under different load conditions. In this study, the performance of Rint, Partnership for a New Generation of Vehicles (PNGV), Thevenin, and Dual Polarization (DP) battery models, which are widely known in the literature, to simulate static and dynamic voltage behavior is compared. A 18650 NMC battery was used for this purpose, and Hybrid Pulse Power Characterization (HPPC), Dynamic Stress Test (DST), Worldwide Harmonised Light Vehicle Test Procedure (WLTP), and Constant Current (CC) discharge tests were performed. The performance of the models for the four tests is compared. The maximum error values for WLTP are 2.98 % in Rint, 1.32 % in PNGV, 2.80 % in Thevenin, and 1.09 % in DP. Comparing the performances of models for all tests, it is found that the DP model is the most accurate model under both constant and dynamic current conditions.

Review of battery models and experimental parameter identification for lithium-ion battery equivalent circuit models

The growing use of electric vehicles has led to an ever-increasing demand for efficient and reliable management systems to control the behavior of lithium-ion batteries, especially with respect to heat generation and state-of-charge. Understanding these patterns constitutes a major new challenge for these batteries, as remaining ignorant of their behavior can result in decreased performance, shorter service life and even safety dangers. This review provides an overview of the different modeling techniques applied to simulate battery behavior. Different methods using equivalent electrical circuit models are discussed, covering both simple battery models and more complex equivalent electrical circuit models, with a focus on the 2RC-Thévenin circuit model. In this context, parameter approach methods for these systems are reviewed. In addition, laboratory tests are run to identify the various model parameters for a lithium-ion battery. This comprehensive study is designed to guide scientists and engineers in the selection and use of suitable tools for state-of-charge and battery health studies.

Novel battery power capability assessment for improved eVTOL aircraft landing

A key aspect in the deployment of electric vertical take-off and landing (eVTOL) aircraft is the safety and performance capabilities of the batteries used. A component of the safety requirements is the need for reserve energy, which would only be utilised in case of emergencies. In the literature, it has been observed that the lower bound of the reserve region of battery energy should be limited to avoid the area where a precipitous drop in voltage would occur. Here, a method for defining the lower bound is proposed. This seeks to extend the amount of time the aircraft can cruise before landing can no longer be completed. A novel power capability testing procedure is used to measure the lowest state-of-charge (SoC) at which a constant power pulse can be completed. This differs from existing power capability tests that perform pulses at predetermined SoC points. The goal of the proposed method is to replicate the conditions of landing to understand the power capability performance at low SoC. The test is performed for a variety of environmental conditions and use cases, which includes temperature and power pulses, as well as two sets of differently aged cells. For the defined test conditions, the lowest SoC values for the calendar aged cells ranges from 6% to 14% SoC, whereas the range for cycle aged cells is 8% to 27% SoC. The outcome of this test is a characteristic map which correlates temperature, pulse power and pulse duration to the lowest SoC the pulse can be completed. The characteristic map indicates the lowest SoC value allowed for the battery before landing needs to be performed. The accuracy of the characteristic map is compared to a battery equivalent circuit model, parametrised from the test data. The defined approaches are experimentally validated based on a set of previously unmeasured experimental conditions. Overall, the characteristic map provides good accuracy compared to measured values, with both map and model methods having an average maximum absolute percentage error of at most 7.5%. Additionally, the test results show that if the worst case landing scenario is used as the lower bound of the reserve region, the useable SoC range for nominal flight would be greatly affected if cell degradation is not considered.

Implementation of Constant Temperature–Constant Voltage Charging Method with Energy Loss Minimization for Lithium-Ion Batteries

Effective charging techniques must consider factors such as charging efficiency, lifecycle, charging time (CT), and battery temperature. Currently, most charging strategies primarily focus on CT and charging losses (CL), overlooking the crucial influence of battery temperature on battery life. Therefore, this study proposes a constant temperature–constant voltage (CT-CV) charging method based on minimizing energy losses. The charging process is primarily divided into three stages. In the first stage, a constant current (CC) charging is implemented using a 2C rate that aims to expedite battery charging but may result in a rapid temperature increase. The second stage involves constant temperature charging, where the charging current is regulated based on battery temperature feedback using a PID controller to maintain a stable battery temperature. The third stage is constant voltage (CV) charging, where a fixed current is applied continuously until the current drops below the charging cutoff current. After completion of the charging process, the charging time can be calculated, and charging losses can be determined by incorporating the battery equivalent circuit model (ECM). To determine the optimal transition time, the paper employs Coulomb counting and the battery ECM, considering both CT and losses to simulate the transition time with minimal CL. This approach achieves optimization of transition points by establishing ECM, measuring internal impedance of the battery, and simulating various charging scenarios, and eliminates the need for multiple actual experiments. Experimental results show that the charging time (CT) should be reduced and the maximum temperature rise (TR) should be reduced under the same average TR condition of the proposed method. At the same CT, the average TR and the maximum TR should both decrease. The charging method proposed in this study exhibits the following advantages: (1) simultaneous consideration of the battery’s equivalent circuit model and charging time; (2) the achieved transition point demonstrates characteristics of minimized charging losses; (3) eliminates the need for multiple experimental iterations.

Research on frequency regulation strategy of battery energy storage system supporting power system

Due to the large-scale grid connection of new energy, the inertia of the power system has decreased, seriously affecting the frequency stability of the power grid, and there is an urgent need for effective frequency support technology. In response to the above issues, this article proposes a frequency control strategy for battery energy storage systems to support power systems. Firstly, establish a battery equivalent circuit model to simulate the dynamic and static performance as well as external characteristics of the battery; Secondly, two frequency modulation strategies, droop control and accelerated droop control, are used to control the active power emitted by the battery energy storage system. Finally, a four-machine two-zone system with a 25% proportion of wind power was built using MATLAB for simulation analysis in two scenarios: sudden reduction of wind power and rapid fluctuation of wind power. The results showed that the frequency modulation strategy proposed in this paper can effectively improve the lowest and stable point frequencies of the system, and can slow down the rate of frequency decline, thereby improving the frequency stability of the power grid.

A modified high C-rate battery equivalent circuit model based on current dependence and concentration modification

The current battery equivalent circuit models are mainly suitable for room temperature or low C-rate conditions. However, the polarization phenomenon is serious at high C-rate, which results in the obvious voltage drop and significantly reduces the model accuracy at high C-rate. In this paper, the characteristics analysis of different RC models is firstly studied. It is found that the first-order RC circuit model is more suitable for high C-rate conditions due to the coupling of model parameter extraction. Based on the first-order RC model, a basic equivalent circuit model adapted to high C-rate condition is then determined. Secondly, the influences of sampling frequency and the identified time domain on instantaneous impedance and polarization resistance are researched. Thirdly, the change rules of different polarizations at high C-rate are analyzed. Furthermore, the relationship between the change rule of the model parameters and that of different overpotentials are researched. Subsequently, a modified high C-rate model is innovatively established, which considers the current dependence and concentration/temperature modification of instantaneous impedance and polarization resistance. Finally, the accuracy of the modified high C-rate model is verified at 5 °C, 25 °C, and 55 °C, respectively. Results show that the modified high C-rate model can improve the simulation accuracy of the voltage at high C-rate (≤6C), and the mean absolute error (MAE) and Root Mean Squared Error (RMSE) are within 68 mV. Compared with the existing high C-rate model, the accuracy of the modified high C-rate model proposed in this paper is improved and the complexity is also significantly reduced.

Passive, Fractional, Battery Equivalent-Circuit Model in Time and Frequency Domains Part 1: Linear Model

Passive, Fractional, Battery Equivalent-Circuit Model in Time and Frequency Domains Part 1: Linear Model

Research on Optimum Charging Current Profile with Multi-Stage Constant Current Based on Bio-Inspired Optimization Algorithms for Lithium-Ion Batteries

Compared with the conventional constant-current constant-voltage (CC-CV) charging method, the multi-stage constant-current (MSCC) charging method offers advantages such as rapid charging speed and high charging efficiency. However, MSCC must find the optimal charging current profile (OCCP) in order to achieve the aforementioned benefits. Hence, in this paper, five bio-inspired optimization algorithms (BIOAs), including particle swarm optimization (PSO), modified PSO (MPSO), grey wolf optimization (GWO), modified GWO (MGWO), and the jellyfish search algorithm (JSA), are applied to solve the problem of searching for the OCCP of the MSCC. The best solution-finding procedure is run on the MATLAB platform developed based on minimizing the objective function of combining charging time (CT) and energy loss (EL) with a proportional weight. Without requiring numerous and time-consuming actual charge-and-discharge experiments, a wide range of searches can be quickly achieved only through the battery equivalent circuit model (ECM) established. The theoretical derivation and correctness are confirmed via the simulation and experimental results, which demonstrate that the OCCPs obtained by using the devised charging strategies possess the shortest CT and the best charging efficiency (CE), and among them, MPSO has the best fitness value (FV). Compared with the traditional CC-CV method, the experimental results show that the maximum improvement rates (IRs) of the studied approaches in terms of six charging performance evaluation indicators (CPEIs), including CT, charging capacity (CHC), CE, charging energy (CWh), average temperature rise (ATR), and FV, are 21.10%, 0.40%, 0.24%, 2.85%, 18.86%, and 68.99%, respectively. Furthermore, according to the comprehensive evaluation with CPEIs, the top three with the best overall performance are the JSA, MPSO, and GWO methods, respectively.

Variable recursive least square algorithm for online battery equivalent circuit model parameters identification for electric vehicles

Variable recursive least square algorithm for online battery equivalent circuit model parameters identification for electric vehicles

A generalized equivalent circuit model for lithium-iron phosphate batteries

Most of the equivalent circuit battery models available in the literature have been developed specifically for one cell and require extensive measurements to calibrate cell electrical parameters in different operating conditions. In this work, a generalized equivalent circuit model for lithium-iron phosphate batteries is proposed, which only relies on the nominal capacity, available in the cell datasheet. Using data from cells previously characterized, a generalized zeroth-order model is developed. This novel approach allows to avoid time-consuming and expensive experiments and reduces the test matrix. In spite of not relying on detailed data on the dependence of the electrical parameters with respect to state of charge, c-rate and temperature, the model provides an excellent description of the electrical behavior for both low-energy and high-energy cells, the error being always kept below 2 %. The internal resistance of the cell is expressed as a function of a new characteristic coefficient, which is typical of this lithium-ion battery chemistry. This coefficient is fitted to an exponential function of the temperature, which is physically meaningful, as the internal resistance has an Arrhenius-like behavior with respect to temperature. This model, due to its simplicity and flexibility, is particularly useful for control-oriented applications, and for off-line analyses.

A lithium-ion battery equivalent circuit model based on a hybrid parametrization approach

This paper proposes an improved lithium-ion battery equivalent circuit model that can simulate the current-voltage characteristics of the battery under various operating conditions. Specifically, a hybrid parametrization approach is adopted by combining the electrochemical impedance spectroscopy and the hybrid pulse power characterization techniques for the identification and quantification of all loss contributions in a lithium-ion battery cell, for a wide operating frequency range. Moreover, the proposed equivalent circuit model considers the variation of the state of charge, the temperature and the charging-discharging current, and since it can be easily realized by utilizing the existing hardware for the cell equalization, it can be a useful tool for a wide range of real-time applications. The above are realized based on analytical equations of the battery performance with respect to the aforementioned operating parameters' variations. The effectiveness and feasibility of the proposed model is experimentally verified on a commercial, high energy capacity cylindrical lithium-ion battery cell of 3.25 Ah by comparing the model voltage performance with the real voltage of the cell during dynamic operating conditions and with variable surface temperature values.

A novel fault diagnosis method for battery energy storage station based on differential current

Nowadays, an increasing number of battery energy storage station (BESS) is constructed to support the power grid with high penetration of renewable energy sources. However, many accidents occurred in BESSs threaten the development of the BESS, so it is important to develop a protection method for the BESS. In this work, a novel fault diagnosis method based on differential current is proposed, which can identify the short circuit fault rapidly and effectively. Firstly, in order to simulate the short circuit fault characteristic of a BESS, a linear varying parameter battery equivalent circuit model (ECM) which can demonstrate the short circuit current are established based on the manta ray foraging optimization (MRFO) algorithm. Secondly, the fault diagnosis method based on differential current is proposed and analyzed through the calculation of short circuit current (SCC) in BESS. Finally, different working state data of battery are used to verify the fault diagnosis method. The results show that the proposed method can effectively diagnose the short circuit fault. In summary, the proposed fault diagnosis method based on differential current is efficient in protecting the BESS.

Cloud-Based Optimization of a Battery Model Parameter Identification Algorithm for Battery State-of-Health Estimation in Electric Vehicles

Connectivity and cloud computing are key elements in the future of electric mobility. They allow manufacturers to provide advanced fleet management and predictive diagnostic services. In particular, cloud computing dramatically enhances data availability and enables the use of more complex and accurate state estimation algorithms for electric vehicle lithium-ion batteries. A tuning procedure for a moving window least squares algorithm to estimate the parameters of a 2-RC equivalent circuit battery model is presented in this paper. The tuning procedure uses real data collected from a test vehicle and uploaded to the Stellantis-CRF cloud. The tuned algorithm was applied to eight months of road tests and showed very small estimation errors. The errors are comparable to other literature data, even when the literature results were obtained in laboratory tests. The estimated model parameters are tracked through time and seem accurate enough to show the first signs of battery aging.

A battery capacity estimation method based on the equivalent circuit model and quantile regression using vehicle real-world operation data

Battery capacity estimation is critical for evaluating the battery performance and safety. Currently, the sampling interval of battery operation data on the cloud is 10–30 s, and relatively poor data quality poses difficulties in battery capacity estimation. In this study, a battery capacity estimation method is proposed based on the battery equivalent circuit model and a quantile regression method using real-world vehicle operation data on the cloud. The battery parameters were identified based on the Thevenin battery model, and the state of charge (SOC) was estimated using a joint Kalman filter. Then, the discharge electric quantity–SOC data was fitted using quantile regression to obtain the preliminary capacity estimation results. To describe the battery capacity degradation along with driving mileage, this estimation result was further fitted using the Arrhenius empirical aging model and another quantile regression. The Nelder–Mead method was used to estimate the coefficients in quantile regression-related algorithms. Because quantile regression is not sensitive to the outliers of data points, it can reduce the impact of poor data quality on battery capacity estimation results. The proposed battery capacity estimation method was verified using real-world vehicle operation data, and the capacity estimation errors were within 3.2%.

Adaptive Constant-Current/Constant-Voltage Charging of a Battery Cell Based on Cell Open-Circuit Voltage Estimation

This paper presents the novel design of a constant-current/constant-voltage charging control strategy for a battery cell. The proposed control system represents an extension of the conventional constant-current/constant-voltage charging based on the so-called cascade control system arrangement with the adaptation of the battery charging current based on the open-circuit voltage parameter estimation. The proposed control strategy features two feedback controllers of the proportional-integral type responsible for: (i) controlling the battery open-circuit voltage towards its fully charged state, and (ii) simultaneously limiting the battery terminal voltage to avoid the battery terminal voltage constraint violation. The open-circuit voltage on-line estimation is implemented by using the system reference adaptive model approach to estimate the linear time-invariant battery equivalent circuit model parameters, whose asymptotic convergence is guaranteed according to Lyapunov stability theory. The proposed concept of the battery charging control is verified by means of simulations using the experimentally obtained model of a lithium iron phosphate battery cell, and it is also compared to other charging methods with respect to charging speed-up potential compared to conventional charging. The proposed method, which can be easily extended to conventional chargers, results in 23.9% faster charging compared to conventional charging, thus representing an inexpensive and straightforward upgrade to conventional battery charging systems.