State Of Power Estimation Research Articles

Joint estimation of state-of-charge and state-of-power for hybrid supercapacitors using fractional-order adaptive unscented Kalman filter

As a new type of energy storage device, hybrid supercapacitors have the advantages of both lithium-ion batteries and supercapacitors. State of charge and state of power estimation are crucial for system operation and energy management. This work proposes a joint estimation method for the state-of-charge (SoC) and state-of-power (SoP) of hybrid supercapacitors based on a fractional-order model and unscented Kalman filter algorithm. Firstly, a parameter identification method for second-order fractional-order models is proposed using a competitive learning-based particle swarm optimization algorithm. On this basis, a SoC estimation method is designed based on the fractional-order adaptive unscented Kalman filter. Then, a SoP estimation method considering multiple constraint conditions is proposed. Finally, the proposed parameter identification and state estimation algorithms are validated under different operating dynamic conditions and environmental temperatures. The experimental results show that the error of model voltage is lower than 100 mV and the SoC estimation error is lower than 2% in the vast majority of cases, which proves the proposed algorithms have good accuracy and robustness in different environments.

An EV-Scale Demonstration of In-Situ Battery Electrochemical Impedance Spectroscopy and BMS-Limited Pack Performance Analysis

State-of-Power (SOP) and State-of-Charge (SOC) estimation inaccuracy manifests throughout the EV battery lifetime due to the non-linear degradation trajectory that is unique to each use-case. The inaccuracy leads to premature termination of charge and discharge operations, which results in the virtual loss of battery performance. In-situ Electrochemical Impedance Spectroscopy (EIS) has been proposed to provide real-time battery impedance measurements, which can theoretically improve the SOP/SOC estimation accuracy. In this work, an EV-scale in-situ EIS system is demonstrated experimentally, from impedance measurement to Equivalent Circuit Model (ECM) extraction. The pack-level discharge energy versus SOP/SOC estimation errors is also simulated, which quantifies the virtual loss of battery performance. The measured-impedance error tolerance of three common ECM extraction techniques is then examined through a randomised set of simulated EIS tests with injected measurement noise. Finally, in-situ impedance measurement is performed on 20 battery sub-modules using an electric pickup truck EIS system. The ECM-predicted voltage output is compared against measured driving data. Experimental results indicate approximately 8-9% improvement in SOP estimation accuracy at 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> C and 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> C between the in-situ extracted models and a representative baseline.

A novel M-1 structured Bidirectional Long Short Term Memory-Rauch Tung Striebel Smoothing algorithm for the joint estimation State of Charge and multi-constrained sustained peak power of lithium-ion batteries

The estimation of State of Charge (SoC) and State of Power (SoP) of lithium-ion batteries is an important part of battery management system. For the purpose of obtaining high-precision SoC and SoP estimation results, this paper proposes a novel M-1 structured Bidirectional Long Short Term Memory-Rauch Tung Striebel Smoothing (BiLSTM-RTSS) algorithm, which can effectively fit current, voltage, temperature and SoC by using the improved sliding window M-1 technique. The RTSS algorithm is applied to update the SoC estimation of the BiLSTM to facilitate the accuracy and speed of SoC estimation. Subsequently, to better estimate the SoP with duration of 30 s, 2 min, and 4 min, three key constraints including SoC estimation results, second-order RC model and battery limits, are simultaneously used in SoP estimation. According to experiment, the mean absolute error of SoC is 0.602, 0.619 and 0.548, 0.469 respectively, under the conditions of HPPC and BBDST. When the duration is 30s, the peak charging and discharging currents up to 170 A and 380 A. In addition, the estimation trends of sustained peak power and peak current are in the same direction. The experimental results verify the rapidity and reliability of the proposed algorithm for SoC and SoP.

Research on Multi-Time Scale SOP Estimation of Lithium–Ion Battery Based on H∞ Filter

Battery state of power (SOP) estimation is an important parameter index for electric vehicles to improve battery utilization efficiency and maximize battery safety. Most of the current studies on the SOP estimation of lithium–ion batteries consider only a single constraint and rarely pay attention to the estimation of battery state on different time scales, which can reduce the accuracy of SOP estimation and even cause safety problems. In view of this, this paper proposes a multi-time scale and multi-constraint SOP estimation method for lithium–ion batteries based on H∞ filtering. Firstly, a second-order RC equivalent circuit model is established with a ternary lithium–ion monolithic battery as the research object, and parameter identification is performed by using the recursive least squares method with a forgetting factor. Secondly, the H∞ filtering algorithm is applied to estimate the state of charge (SOC), and then the joint multi-time scale multi-constrained SOC-SOP estimation is performed. Finally, the joint estimation algorithm is validated under UDDS conditions. The mean absolute value relative error (MARE) of SOC estimation is 1.17%, and the MARE of SOP estimation at different time scales is less than 1.6%. The results indicate the high accuracy and strong robustness of the joint estimation method.

Experimental Investigation of Voltage Limitation Modes and State of Power Estimation for a High-Power Lithium-Ion Battery

This paper investigates the behaviour of a high-power lithium-ion battery (LIB) pouch cell under voltage limitation at a high state of charge (SOC). The state of power (SOP) estimation is crucial in providing insights into optimising energy recovery during regenerative braking events. Experiments were conducted at different high-charging C-rates to analyse the voltage limitation modes and to assess the accuracy of a model-based SOP estimation algorithm developed based on published literature. The results show that the accuracy of the battery model alone is not sufficient to address the accuracy of the SOP estimation algorithm. Furthermore, different voltage limitation modes are discussed and the average power output is investigated. For example, it was observed that Constant-Current Constant-Voltage (CCCV) mode outputs 59.75% more power than Constant-Current (CC) pulses. These findings provide valuable insights into the behaviour of high-power LIB pouch cells and offer a foundation for further research to improve regenerative braking performance for motorsport applications.

A Model Fusion Method for Online State of Charge and State of Power Co-Estimation of Lithium-Ion Batteries in Electric Vehicles

In this paper, a model fusion method (MFM) is proposed for online state of charge (SOC) and state of power (SOP) co-estimation of lithium-ion batteries (LIBs) in electric vehicles (EVs). Firstly, a particle swarm optimization-genetic algorithm (PSO-GA) method is cooperated with a 2-RC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CPE</sub> fractional-order model (FOM) to construct battery open-circuit voltage (OCV)-SOC curve, which only relies on a part of dynamic load profile without the prior knowledge of an initial SOC. Secondly, a dual extended Kalman filter (DEKF) algorithm based on a 1-RC model is employed to identify the model parameters and estimate battery SOC with the extracted OCV-SOC curve. Furthermore, battery polarization dynamics in a SOP prediction window is analyzed from two aspects: (1) self-recovery; and (2) current excitation. They are separately simulated using 2-RC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CPE</sub> FOM and 1-RC model, and then integrated through a model fusion for online SOP estimation, which enables an analytical expression of battery peak charge/discharge current in a prediction window without weakening the nonlinear characteristic of FOM. Experimental results demonstrate the improved performance of the proposed MFM for online discharge SOP estimation, where the mean absolute error and root mean square error are only 0.288 W and 0.35 W, respectively, under the urban dynamometer driving schedule profile.

Online state of charge and state of power co-estimation of lithium-ion batteries based on fractional-order calculus and model predictive control theory

Accurate battery modelling is the cornerstone to state of charge (SOC) and state of power (SOP) co-estimation of lithium-ion batteries in electric vehicles. Due to strong battery nonlinearity over a broad frequency range, traditional integer-order models are incapable of capturing complex battery dynamics for SOC and SOP co-estimation. This paper proposes a fractional-order modified moving horizon estimation (FO-mMHE) algorithm and a fractional-order model predictive control (FO-MPC) algorithm. Firstly, a second-order FOM is constructed by performing a series of hybrid pulse tests at different SOC regions, and its model parameters are identified through a particle swarm optimization-genetic algorithm method. Secondly, online SOC estimation is converted into a constrained optimization problem in a past moving horizon and then solved by the FO-mMHE algorithm, which enables fast convergence speed and proactive smoothing of estimation outcomes. Thirdly, the FO-MPC algorithm is devised to manipulate the current sequence in a prediction horizon for maximizing discharge/charge power accumulation and determining battery SOP in real time. Moreover, different battery current–voltage behaviors are comprehensively researched in the prediction horizon over a whole battery operating range. The proposed co-estimation method is validated under different dynamic load profiles. The experimental results demonstrate a SOC estimation error reduction of up to 1.2 % compared with the commonly used fractional-order extended Kalman filter while the SOP estimation error could be limited below 0.35 W.

Nonlinear Optimization Strategy for State of Power Estimation of Lithium-Ion Batteries: A Systematical Uncertainty Analysis of Key Impact Parameters

The state of power (SOP) of lithium-ion batteries plays an essential role in power distribution of electric vehicles and energy storage stations. However, due to the highly nonlinear dynamic behaviors and the parameter errors, accurate and reliable SOP estimation is always difficult. This article develops an optimization strategy to estimate SOP, in which the multiple constraints are simultaneously considered and the nonlinear equivalent circuit model (ECM) is directly adopted. On basis of it, the effects of single parameter uncertainty and multiparameter uncertainty are thoroughly investigated. The results show that compared to the conventional method, the proposed method could provide more reliable SOP estimation during the whole operation range. Moreover, different uncertainty sources have different effects on estimation results, not only the estimate values but also the constraint regions. This is the first time to directly employ the nonlinear form of ECM parameters in the SOP estimation and provide a comprehensive investigation of various uncertainty sources.

Model Development for State-of-Power Estimation of Large-Capacity Nickel-Manganese-Cobalt Oxide-Based Lithium-Ion Cell Validated Using a Real-Life Profile

This paper investigates the model development of the state-of-power (SoP) estimation for a 43 Ah large-capacity prismatic nickel-manganese-cobalt oxide (NMC) based lithium-ion cell with a thorough aging investigation of the cells’ internal resistance increase. For a safe operation of the vehicle system, a battery management system (BMS) integrated with SoP estimation functions is crucial. In this study, the developed SoP model used for the estimation of power throughout the lifetime of the cell is coupled with a dual-polarization equivalent-circuit model (DP_ECM) for achieving the precise estimation of desired parameters. The SoP model is developed based on the pulse-trained internal resistance evolution approach, and hence the power is estimated by determining the rate of internal resistance increase. Hybrid pulse power characterization (HPPC) test results are used for extraction of the impedance parameters. In the DP_ECM, Coulomb counting and extended Kalman filter (EKF) state estimation methods are developed for the accurate estimation of the state of charge (SoC) of the cell. The SoP model validation is performed by using both dynamic Worldwide harmonized Light vehicles Test Cycles (WLTC) and static current profiles, achieving promising results with root-mean-square errors (RMSE) of 2% and 1%, respectively.

A data-model fusion method for online state of power estimation of lithium-ion batteries at high discharge rate in electric vehicles

This paper proposes a novel data-model fusion method (DMFM) for online state of power (SOP) estimation of lithium-ion batteries at high discharge rates in electric vehicles. First, battery polarisation characteristics responding for high discharge rates are experimentally investigated through a series of decremental pulse tests. Battery polarisation voltage is observed with diverse growing patterns over a whole battery operation range, and its underlying correlations with state of charge (SOC), discharge rate and pulse runtime are recognised. Second, a feed-forward neural network (FFNN) with SOC, discharge rate and pulse runtime as inputs, is constructed to characterise battery polarisation voltage through modelling the current excited polarisation resistance. Third, a DMFM is proposed to combine the data-driven method and equivalent-circuit model based method for accurate online SOP estimation in a lengthy prediction window ranging from 30 s to 120 s. Moreover, an unscented Kalman filter is devised to filter the estimation outcomes of the DMFM for noise suppression. The experimental results validate the effectiveness of the constructed FFNN in reproducing the nonlinearity of battery polarisation characteristics at high discharge rates and show the significant improvement in SOP estimation accuracy.

Online joint estimator of key states for battery based on a new equivalent circuit model

Accurate estimation of the key states of batteries is essential for safe and reliable battery operation. In this paper, a joint estimation method for state of health (SOH), state of charge (SOC) and state of power (SOP) of batteries based on the autoregressive equivalent circuit model (AR-ECM) is proposed. Firstly, considering the coupling relationship existing between these key states of the battery, the state space-coupling model based on AR-ECM is proposed. Then, by analyzing the different characteristics of the model parameters, a differentiated model parameter identification strategy is proposed. Finally, based on the accurate estimation of the model parameters, the square root unscented Kalman filter (SR-UKF) is used to realize the online estimation of SOH and SOC. The SOP estimation under multiple constraints is realized based on the updated state, voltage, and current. Experimental results in noise free and Gaussian white noise environments show that the multi-state joint estimation algorithm has high estimation accuracy and robustness.

Research on State of Power Estimation of Echelon-Use Battery Based on Adaptive Unscented Kalman Filter

An echelon-use lithium-ion battery (EULB) refers to a powered lithium-ion battery used in electric vehicles when the battery capacity is attenuated to less than 80% and greater than 20%. Aiming at the degradation of the performance of the EULB and the unclear initial value of the state of energy (SOE), estimations of the state of power (SOP) of an EULB are not accurate. An SOP estimation method based on an adaptive dual unscented Kalman filter (ADUKF) is proposed. First, the second-order resistor-capacitance symmetry equivalent model (SRCSEM) of the EULB is established. Second, an unscented transformation (UT) is introduced and the battery parameters estimated by the ADUKF: (a) the SOE is estimated based on an adaptive unscented Kalman filtering (AUKF) algorithm, that uses the observation noise equation γk, Rk and the processes noise equation qk, Qk, and (b) the ohmic internal resistance (OIR) and actual capacity (AC) are estimated based on the aforementioned algorithm, which uses the observation noise equation γθ,k, Rθ,k and the process noise equation qθ,k, Qθ,k. Third, the working voltage and OIR are predicted using optimal estimation, and the SOP of the EULB is estimated. MATLAB simulation results show that EULB symmetry capacity decays to 80%, 60%, 40%, and 20% of rated capacity, the proposed algorithm is adaptive regardless of whether the initial SOE value is consistent with the actual value, and the estimation error of the EULB’s SOP is less than 3.28%, showing high accuracy. The results of this study can provide valuable reference for estimating EULB parameters, and help to understand the usage behavior of retired batteries.

An enhanced multi-constraint state of power estimation algorithm for lithium-ion batteries in electric vehicles

In this paper, an enhanced multi-constraint (MC) state of power (SOP) estimation algorithm in a prediction window up to 120 s is developed for lithium-ion batteries in electric vehicles (EVs). First, a novel regression-based algorithm (RBA) incorporating a model parameter forward prediction is devised for voltage-constraint SOP estimation to reduce battery linearization error and improve model accuracy by estimating model parameters to the end of a prediction window. The convergence condition is analytically formulated and can be satisfied over a whole battery operating range. Second, an improved state of energy (SOE)-constraint SOP estimation algorithm is proposed from a more practical perspective by considering battery terminal voltage variation in a prediction window. Together with the other constraints, the enhanced MC SOP estimation algorithm is achieved, which specifies a dynamic safe operating area for power regulation in EVs. Moreover, an incremental pulse test is designed to obtain reference SOPs in high fidelity under static conditions and dynamic load profiles. Simulations and experimental results demonstrate the improved accuracy of the enhanced MC SOP estimation algorithm over the conventional MC online SOP estimation algorithm.

State of power estimation of power lithium-ion battery based on an equivalent circuit model

State of power (SOP) is the maximum power that can be released or absorbed steadily by the power battery within a predetermined time interval. In order to provide stable and reliable output power for electric vehicles as well as ensure the safety of electric vehicles within a certain period of time, SOP estimation plays a very important role in the battery management system. SOP shows how quickly people can add energy to or remove energy from the battery without violating a set of design constrains. On the basis of a Rint model, this paper proposes a SOP estimation method based on two assumptions, and proves it in detail. The experimental results verify the model and the algorithm under various working conditions and temperatures as well as giving analysis and comparison. When the time period ∆T = 70min, the mean absolutely error (MAE) is less than 1.6 W for charging SOP estimation and less than 4.1 W for discharging SOP estimation respectively. Moreover, the affected of the predictive time on SOP estimation result is also studied.

Model‐based state of X estimation of lithium‐ion battery for electric vehicle applications

In developing an efficient battery management system (BMS), an accurate and computationally efficient battery states estimation algorithm is always required. In this work, the highly accurate and computationally efficient model-based state of X (SOX) estimation method is proposed to concurrently estimate the different battery states such as state of charge (SOC), state of energy (SOE), state of power (SOP), and state of health (SOH). First, the SOC and SOE estimation is performed using a new joint SOC and SOE estimation method, developed using a multi-time scale dual extended Kalman filter (DEKF). Then, the SOP estimation using T-method and 2RC battery model is performed to evaluate the non-instantaneous peak power during charge/discharge. Finally, the battery current capacity estimation is performed using a simple coulomb counting method (CCM)-based capacity estimation with a sliding window. The performance of the proposed SOX estimation method is compared and analyzed. The experimental results show that the estimated SOC and SOE error is less than 1% under considered dynamic load profile at three different temperatures. After the final convergence, the estimated capacity maximum value absolute error is ±0.08 Ah. In addition, the low value of evaluated mean execution time (MET) justifies the high computational efficiency of the proposed method.

Electrochemical impedance characteristics at various conditions for commercial solid–liquid electrolyte lithium-ion batteries: Part. 2. Modeling and prediction

Solid–liquid electrolyte lithium-ion batteries (SLELBs) have good commercial viability in electric vehicle applications because they combine the safety of solid electrolyte lithium-ion batteries with the high ionic conductivity of liquid electrolyte lithium-ion batteries (LELBs). The safe and efficient operation of electric vehicles is inseparable from the key battery management algorithms such as battery state of charge (SOC), state of health and state of power estimation. In the process of designing battery management algorithms for SLELBs, it is essential to have an accurate understanding of battery behavior under different influencing factors and to build a high-fidelity battery simulation model. Electrochemical impedance spectroscopy (EIS) can be used to study the electrode process dynamics and ion transport mechanism in lithium-ion batteries. It is an urgent challenge to use EIS to experiment and analyze the characteristic impedances of SLELBs under the full-scale factors and to construct the battery model and simulate the battery impedance under the premise of a reasonable number of tests.In this series of two papers, we first propose a regression model of temperature and SOC One-Way factor SLELB characteristic impedances through a full-scale experimental design under the theoretical framework of experimental optimization design and statistical analysis. Then, in order to construct the model under the premise of a reasonable number of tests, an orthogonal experiment is designed and an orthogonal piecewise polynomial Arrhenius-simplified equivalent circuit model (SECM) for SLELB impedance prediction of the Two-Way factor of temperature and SOC is established. These models can accurately describe SLELB behavior under different factors, improve the understanding of SLELB electrode processes, and predict the impedance spectrum of SLELB, all of which support the key battery management algorithms. In the first paper, the characteristic impedances in the EIS were identified to facilitate a systematic analysis at different temperatures and SOCs in a full-scale experimental design. The Arrhenius and polynomial regression models of the One-Way factor SLELB characteristic impedances of temperature and SOC were established.In this second paper, an equivalent circuit model (ECM) based on the first principles of the electrode process of SLELB is established and simplified according to the EIS impedance frequency range to obtain the SECM. In order to construct the battery model under the premise of a reasonable number of experiments, we design an orthogonal experiments scheme to reduce the number of experiments to half that of the full-scale experiments. An orthogonal piecewise polynomial Arrhenius (OPPA) temperature and SOC Two-Way factor parameter model is established using ANOVA considering the interaction of the ECM model parameters. The experimental results show that OPPA has an accurate prediction performance for ECM parameters with a reasonable number of segments and orders. The predictive performance of OPPA-SECM is similar to that of full-scale piecewise polynomial Arrhenius (FPPA)-SECM, and the number of OPPA-SECM experiments is reduced by half that of FPPA-SECM experiments.

Model Development for State of Power Estimation of Nmc-Based Lithium-Ion Cell Validated Using Real-Life Profile

Model Development for State of Power Estimation of Nmc-Based Lithium-Ion Cell Validated Using Real-Life Profile

Electrochemical impedance characteristics at various conditions for commercial solid–liquid electrolyte lithium-ion batteries: Part 1. experiment investigation and regression analysis

Solid–liquid electrolyte lithium-ion batteries (SLELBs) have good commercial viability in electric vehicle applications because they combine the safety of solid electrolyte lithium-ion batteries with the high ionic conductivity of liquid electrolyte lithium-ion batteries (LELBs). The safe and efficient operation of electric vehicles is inseparable from the key battery management algorithms such as battery state of charge (SOC), state of health and state of power estimation. In the process of designing the battery management algorithms for SLELBs, it is essential to have an accurate understanding of battery behavior under different influencing factors and build a high-fidelity battery model. Electrochemical impedance spectroscopy (EIS) can be used to study the electrode process dynamics and ion transport mechanism in lithium-ion batteries. However, it can be a huge challenge to use EIS to experiment and analyze the characteristic impedances of SLELBs under the full-scale factors, and to construct the battery model and simulate the battery impedance under the premise of a reasonable number of tests.Over a series of two papers, we first propose a regression model of temperature and SOC One-Way factor SLELB characteristic impedances through full-scale experimental design under the theoretical framework of experimental optimization design and statistical analysis. Then, in order to construct the model under the premise of a reasonable number of tests, the orthogonal experiment is designed, and the orthogonal piecewise polynomial Arrhenius - simplified equivalent circuit model for SLELB impedance prediction of the Two-Way factor of temperature and SOC is established. These models can accurately describe SLELB behavior under different factors, improve the understanding of the SLELB electrode process, and predict the impedance spectrum of SLELB, support the key battery management algorithms.In this first paper, EIS is used to analyze the electrode process kinetics of Li7La3Zr2O12 SLELBs at different temperatures and SOCs in a full-scale experimental design. Furthermore, the characteristic impedances in the EIS are identified to facilitate a systematic analysis of the battery performance. The Arrhenius model and polynomial model are used to perform the regression analysis of temperature and SOC One-Way factor SLELB characteristic impedances. Experimental results show that these models can achieve a high precision regression for One-Way factor characteristic impedances.

A Review of Equivalent Circuit Model Based Online State of Power Estimation for Lithium-Ion Batteries in Electric Vehicles

With rapid transportation electrification worldwide, lithium-ion batteries have gained much attention for energy storage in electric vehicles (EVs). State of power (SOP) is one of the key states of lithium-ion batteries for EVs to optimise power flow, thereby requiring accurate online estimation. Equivalent circuit model (ECM)-based methods are considered as the mainstream technique for online SOP estimation. They primarily vary in their basic principle, technical contribution, and validation approach, which have not been systematically reviewed. This paper provides an overview of the improvements on ECM-based online SOP estimation methods in the past decade. Firstly, online SOP estimation methods are briefed, in terms of different operation modes, and their main pros and cons are also analysed accordingly. Secondly, technical contributions are reviewed from three aspects: battery modelling, online parameters identification, and SOP estimation. Thirdly, SOP testing methods are discussed, according to their accuracy and efficiency. Finally, the challenges and outlooks are presented to inspire researchers in this field for further developments in the future.

Estimation of state-of-power capability for lithium-ion battery considering limiting conditions recalibration

ABSTRACT As one of the most significant deciding factors for energy management systems (EMSs) and battery management systems (BMSs) in electrified vehicles, battery state-of-power (SOP) estimation is an area of interest in battery research. Battery model parameters change obviously under the limiting working condition of SOP, and the available maximum current and state-of-charge (SOC) have to be updated for accurate SOP estimation. This paper tries to contribute to the existing literature as follows: Based on Thevenin model, recursive least-square (RLS) and H-infinity filter algorithm are adopted for parameter identification and SOC estimation for a recalibration purpose to improve the prediction of battery SOP under variable degradation. Multi-constraints are firstly adopted to calculate the limiting current, and the response function of capacity loss-temperature-discharge rate is brought back to correct the actual capacity at this current for the revised limiting current with consideration of weight distribution ratio. Finally, the experiment verifies that the final maximum charging-discharging current modifies the initial calculation value by 5% and 4%, and realizes the more accurate online SOP estimation. This method provides a more accurate and reliable SOP estimation method for electric vehicles.