Adaptive State Of Charge Estimator Research Articles

Improved Backward Smoothing Square Root Cubature Kalman Filtering and Fractional Order—Battery Equivalent Modeling for Adaptive State of Charge Estimation of Lithium‐Ion Batteries in Electric Vehicles

The accuracy of lithium‐ion battery state of charge (SOC) estimation affects the driving distance, battery life, and safety performance of electric vehicles. Herein, the polarization reaction inside the battery is modeled using a second‐order fractional‐order equivalent circuit model and uses an adaptive genetic algorithm for model parameter identification. Then, an improved adaptive fractional‐order backward smoothing square root cubature Kalman filtering algorithm (AFOBS‐SRCKF) is proposed by integrating Sage Husa adaptive filtering and backward smoothing processes to optimize the square root cubature Kalman filter for improving the accuracy and adaptability of real‐time estimation of SOC in a complex environment. Finally, the algorithm is compared with the integer‐order SRCKF, fractional‐order SRCKF through simulation, and fractional‐order backward smoothing SRCKF through simulation. Under complex operating conditions, the error sum of SOC estimation of the AFOBS‐SRCKF algorithm is controlled within 1.0% and the convergence speed is improved by at least 30%. The results show that the AFOBS‐SRCKF algorithm effectively improves the accuracy, stability, and convergence of SOC estimation.

Adaptive state of charge estimation for lithium‐ion batteries using feedback‐based extended Kalman filter

AbstractThe battery management system (BMS) is a crucial component of electric vehicles (EVs) owing to its sustainable operation. To ensure optimal performance of the BMS, state of charge (SOC) of the equipped battery is required to be effectively and accurately estimated. In this paper, the authors consider high‐order equivalent circuit model (ECM) to capture the dynamic characteristics of lithium‐ion batteries, which are connected in series with internal resistance by 2‐RC networks. The parameters of the RC network are determined by mathematically solving the working conditions of the two states. Moreover, the parameters of the battery can be derived by hybrid pulse power characterization (HPPC) tests. Then, based on the open‐circuit voltage, the proposed feedback‐based extended Kalman filtering (FEKF) algorithm is established. The parameters from the simulation have shown that the highest error is 0.0306 V, the optimal knowledge of which can improve the SOC estimation approach remarkably and can provide a reference value. Afterwards, the non‐linear predicting and corrective techniques are applied to the experiment in the extended calculation process. The original error is reduced by the FEKF algorithm, where the maximum and average errors are 0.0298 and 0.0240 V, respectively. Consequently, the established high‐order ECM utilizing the FEKF algorithm may provide SOC estimation with an error of 1.5% or less, resulting in superb performance from the lithium‐ion battery pack.

An adaptive state of charge estimator for lithium‐ion batteries

AbstractThis study presents a data‐driven approach in conjunction with an adaptive extended Kalman filter (AEKF) to estimate lithium‐ion batteries' state of charge (SOC) online. The Thevenin battery model is used to evaluate the effects using battery voltage and current. The advantages of the Lagrange multiplier method are utilized to model the lithium‐ion battery. The Lagrange multiplier method continuously decreases the model error to adjust the Kalman gain of AEKF for accurate SOC estimation. Various current profiles such as hybrid pulse test, dynamic stress test, and Beijing dynamic stress test are used to verify the proposed approach's adaptability, robustness, and accuracy. It is observed that the proposed approach outperforms other methodologies (recursive least square–AEKF and forgetting factor recursive least square–AEKF) due to its high accuracy (mean average error of 0.32%). Additionally, the proposed approach exhibits robustness and high convergence speed despite deliberate erroneous initialization of parameters, thus indicating its applicability in online SOC estimation applications.

On-line WSN SoC estimation using Gaussian Process Regression: An Adaptive Machine Learning Approach

Wireless sensor networks (WSN) are low-resource devices that run on small batteries. The availability of battery energy, device drive cycles, and environmental conditions all have an impact on node lifetime. The state of charge (SoC) is an important factor in determining the amount of energy available in the batteries. Accurate SoC estimation is critical for device lifetime prediction and safe device operation. We present a novel approach for adaptive SoC estimation based on Gaussian Process Regression in this paper (GPR). The training data was obtained in a climate-controlled laboratory setting by using IEEE 802.15.4-based drive loads at various temperatures for three different batteries such as Lithium-Ion, Nickel-metal hydride, and Lithium-Polymer. To estimate the SoC, battery parameters such as voltage, capacity, and temperature were directly mapped to the corresponding models. For each battery parameter, the GPR model with hyper tuned Radial Bias Filter (RBF) was trained at temperatures ranging from 5 °C to 45 °C. For model accuracy, the proposed scheme was compared to polynomial regression and support vector machines (SVM). In this regard, the proposed model provided Mean Absolute Error (MAE) values of 2.53 percent, 2.54 percent, and 2 percent, respectively, and Root Mean Square Error (RMSE) values of 0.295, 0.292, and 0.35 for Nickel-metal hydride, Lithium-Polymer, and Lithium-Ion batteries at 25 °C. Our proposed lightweight GPR scheme is, to the best of our knowledge, the only active implementation on embedded platforms for SoC estimation of WSN. Finally, the model was rigorously tested on ARM Cortex M4-based microcontrollers to report real-time online SoC estimation on WSN nodes.

Adaptive Integral Correction-Based State of Charge Estimation Strategy for Lithium-Ion Cells

Lithium-ion (Li-ion) battery systems are critical elements of future energy systems and electric vehicles. Accurate prediction of the state of charge (SoC) is necessary for the safe and reliable functioning of Li-ion battery systems. Achieving a precise SOC estimate is challenging due to the nonlinear characteristics and variations of model parameters caused over the cell lifetime. This paper introduces an adaptive estimation strategy that can compensate for the effect of cell degradation for achieving high accuracy SoC estimation. The proposed method uses an integral correction-based SoC estimation loop utilizing a Li-ion cell model. The effect of model parameter variation is corrected by introducing two additional correction factors, the cell model resistance, and capacity correction factor. These correction factors are employed to update the Li-ion cell model, resulting in an adaptive integral correction-based SoC estimation technique that can compensate for the influence of cyclic degradation-induced parameter change. The proposed method is validated through extensive simulations in the Matlab-Simulink environment, and its output is compared to the existing unscented Kalman filter-based SoC estimation method. The proposed estimation strategy can adapt to the cell circumstances and correct for model uncertainties. The results indicate that the proposed adaptive SoC estimation strategy provides more precise and accurate SoC estimates for the entire lifespan of the Li-ion cell.

New Artificial Intelligence Technology Applied in Automobile Lithium Battery Manufacturing

In order to improve the estimation accuracy of the state of charge (SOC) of electric vehicle power batteries, this paper is based on artificial intelligence technology for lithium-ion battery model and parameter identification algorithm, adaptive unscented Kalman filter algorithm and SOC estimation based on battery model fusion Algorithm for research. The simulation results show that the SOC error estimated by the artificial intelligence adaptive Kalman filter method is less than 2.4%, which effectively reduces the impact of unknown interference noise on the battery management system when the electric vehicle is driving. The SOC estimation accuracy is higher than that of the extended Kalman method, and has good robustness.

Adaptive State-of-Charge Estimation for Lithium-Ion Batteries by Considering Capacity Degradation

The accurate estimation of a lithium-ion battery’s state of charge (SOC) plays an important role in the operational safety and driving mileage improvement of electrical vehicles (EVs). The Adaptive Extended Kalman filter (AEKF) estimator is commonly used to estimate SOC; however, this method relies on the precise estimation of the battery’s model parameters and capacity. Furthermore, the actual capacity and battery parameters change in real time with the aging of the batteries. Therefore, to eliminate the influence of above-mentioned factors on SOC estimation, the main contributions of this paper are as follows: (1) the equivalent circuit model (ECM) is presented, and the parameter identification of ECM is performed by using the forgetting-factor recursive-least-squares (FFRLS) method; (2) the sensitivity of battery SOC estimation to capacity degradation is analyzed to prove the importance of considering capacity degradation in SOC estimation; and (3) the capacity degradation model is proposed to perform the battery capacity prediction online. Furthermore, an online adaptive SOC estimator based on capacity degradation is proposed to improve the robustness of the AEKF algorithm. Experimental results show that the maximum error of SOC estimation is less than 1.3%.

Adaptive state of charge estimation for lithium-ion batteries based on implementable fractional-order technology

Abstract State of charge (SOC) estimation is of vital importance in battery management systems to ensure both safety and reliability. However, the polarization effect, the stochastic disturbance and the highly nonlinear and dynamic natures throughout the whole lifetime of batteries bring many challenges for accurate online estimation. On account of these difficulties, this paper proposes a novel SOC estimation strategy based on open circuit voltage by means of some implementable fractional-order techniques. Firstly, the fractional-order equivalent circuit model that can reveal more intrinsic electrochemical characteristics of batteries is introduced and parameterized by particle swarm optimization algorithm, then it is combined with particle filter that based on Monte Carlo method for SOC estimation. To achieve rapid convergence and strong robustness, an adaptive noise variance updating algorithm is adopted to update the SOC estimations in particle filter. Moreover, considering the computational burden of fractional-order model, the infinite impulse response filtering technique that adapts to data-driven modeling is introduced to simplify the discrete state space model in estimation. Lastly, the proposed algorithms are implemented in static and dynamic experiments, and the results indicate that the aforementioned strategies can realize fast convergence and precise estimation with applicable calculations.

Hardware-in-the-loop Implementation of ANFIS based Adaptive SoC Estimation of Lithium-ion Battery for Hybrid Vehicle Applications

Abstract This paper presents an effective method to estimate the state of charge (SoC) of a Lithium-ion battery. This parameter is very crucial as it indicates the performance and health of the battery. The battery SoC estimation equivalent circuit provided in MATLAB has been modified by adding the 3- RC pairs in series with its internal resistance. The values of the RC pairs have been calculated mathematically by solving the circuit model, based on charging and discharging dynamics of the battery. The values of these parameters have also been optimized using a “lsqnonlin” function. The SoC of the battery is estimated using the combination of coulomb counting and open-circuit voltage methods to minimize the error in estimation. The obtained SoC is further corrected for errors using ANFIS based algorithms. The effect of temperature has also been accounted for modelling the battery and in SoC estimation. These obtained SoCs for 3 cases, i.e. without RC/with RC pairs and then tuned with ANFIS based optimization are compared for the same load. The parameter calculation method adopted here results in an efficient and accurate model that keeps track of correct battery SoC. The complete system is validated in real-time using hardware-in-the-loop laboratory setup.

A Novel Adaptive SOC Estimation Method for a Series-connectedLithium-ion Battery Pack Under Fast-varying Environment Temperature

This paper proposes a model-based state-of-charge (SOC) estimation method for a series-connected battery pack under fast-varying environment temperature. For accurately evaluating the SOC of the battery pack equipped with passive balance control, the relationship of battery pack and in-pack cell in the available capacity is analyzed. A filtering process is applied to select the alterable reference cell (ARC) for supporting the modeling framework of SOC estimation. An adaptive SOC estimator is presented by using an optimized recursive least squares algorithm to identify all cells parameters, and using an adaptive extended Kalman filter algorithm (AEKF) to estimate the pack generalized SOC in real-time. Furthermore, a bias correction approach is developed to compensate the cell available capacity at low temperature based on the cell resistance of off-line identification and the open-circuit voltage (OCV) of on-line estimation. The experimental verification is conducted through the modified Federal Urban Driving Schedule (FUDS) cycles with environment temperature varying from 25°C to -35°C. Results show that the accuracy of the proposed SOC estimation method is considerably high, and the correction approach can compensate the cell available capacity effectively with acceptable error.

An Online Data-Driven Model Identification and Adaptive State of Charge Estimation Approach for Lithium-ion-Batteries Using the Lagrange Multiplier Method

Reliable and accurate state of charge (SOC) monitoring is the most crucial part in the design of an electric vehicle (EV) battery management system (BMS). The lithium ion battery (LIB) is a highly complex electrochemical system, which performance changes with age. Therefore, measuring the SOC of a battery is a very complex and tedious process. This paper presents an online data-driven battery model identification method, where the battery parameters are updated using the Lagrange multiplier method. A battery model with unknown battery parameters was formulated in such a way that the terminal voltage at an instant time step is a linear combination of the voltages and load current. A cost function was defined to determine the optimal values of the unknown parameters with different data points measured experimentally. The constraints were added in the modified cost function using Lagrange multiplier method and the optimal value of update vector was determined using the gradient approach. An adaptive open circuit voltage (OCV) and SOC estimator was designed for the LIB. The experimental results showed that the proposed estimator is quite accurate and robust. The proposed method effectively tracks the time-varying parameters of a battery with high accuracy. During the SOC estimation, the maximum noted error was 1.28%. The convergence speed of the proposed method was only 81 s with a deliberate 100% initial error. Owing to the high accuracy and robustness, the proposed method can be used in the design of a BMS for real time applications.

Adaptive state of charge estimation of Lithium-ion battery based on battery capacity degradation model

For electric vehicles (EVs), accurate State of Charge (SoC) estimation of battery contributes to ensure battery safety and improve driving mileage. Therefore, its research has essential application value. However, accurate SoC estimation of the battery relies on precise battery model parameters and capacity. This paper mainly carries out three aspects of work. (1) A battery equivalent circuit model is established, and the Forgetting Factor Recursive Least Squares (FFRLS) method is used to realize online identification of model parameters. (2) Based on the Arrhenius equation, the inverse power law equation and the battery capacity degradation equation, the battery capacity degradation model under dynamic stress is established to achieve the online prediction of battery capacity. (3) Based on equivalent circuit model, battery capacity degradation model and Adaptive Extended Kalman Filtering (AEKF) algorithm, an adaptive SoC estimation method is proposed. Simulation results show that the maximum estimation error of battery capacity and SoC is less than 2.5% and 1.5% respectively.

Adaptive State-of-Charge Estimation Based on a Split Battery Model for Electric Vehicle Applications

The conventional state-of-charge (SoC) estimation methods based on the equivalent circuit model (ECM) integrate all state variables into one augmented state vector. However, the correlations between RC voltages and SoC degrade the stability and accuracy of the estimates. To address this problem, this paper presents an adaptive SoC estimation method based on the split battery model, which divides the conventional augmented battery model into two submodels: the RC voltage submodel and the SoC submodel. Hence, the cross interference between RC voltages and SoC is reduced, which effectively reduces the oscillation in the estimation and improves the estimation accuracy. In addition, the adaptive algorithm is applied on the SoC submodel to improve the system robustness to noise disturbances. A case of a second-order ECM is analyzed and two types of Lithium-ion batteries are employed to verify the universality of the proposed method. Experimental results show that the undesired oscillation is eliminated during the convergence stage and the maximum SoC error is within 1% over a wide SoC range.

State of Charge Estimation of Vanadium Redox Flow Battery Based on Sliding Mode Observer and Dynamic Model Including Capacity Fading Factor

State of charge (SOC) of the batteries is a key indicator for battery monitoring and control. Long-term operation of vanadium redox flow batteries may cause ion diffusions across the membrane and the depletion of active materials, which will lead to capacity fading and increase in internal resistance. In previous studies, the capacity fading factor is not considered when designing the SOC estimation observer. This will cause a large error of SOC estimation if the capacity fading is significant. Thus, a selection of an adaptive SOC estimation method considering capacity fading factor is critical. In this paper, an adaptive observer—sliding mode observer—capable of monitoring SOC considering capacity factor is proposed based on a nonlinear electrical model. The observer is designed to adjust the capacity based on the decaying factor and compensate the error caused by the electrical model. A root mean square error of 0.013 V between the measured terminal voltage and estimated voltage is observed while a root mean square error of 0.12 V with the modeled voltage. The mean error between the observed and the modeled capacities is 0.14 Ah. The proposed method shows that the sliding mode observer could accurately estimate SOC with capacity fading.

Improved OCV Model of a Li-Ion NMC Battery for Online SOC Estimation Using the Extended Kalman Filter

Accurate modeling of the nonlinear relationship between the open circuit voltage (OCV) and the state of charge (SOC) is required for adaptive SOC estimation during the lithium-ion (Li-ion) battery operation. Online SOC estimation should meet several constraints, such as the computational cost, the number of parameters, as well as the accuracy of the model. In this paper, these challenges are considered by proposing an improved simplified and accurate OCV model of a nickel manganese cobalt (NMC) Li-ion battery, based on an empirical analytical characterization approach. In fact, composed of double exponential and simple quadratic functions containing only five parameters, the proposed model accurately follows the experimental curve with a minor fitting error of 1 mV. The model is also valid at a wide temperature range and takes into account the voltage hysteresis of the OCV. Using this model in SOC estimation by the extended Kalman filter (EKF) contributes to minimizing the execution time and to reducing the SOC estimation error to only 3% compared to other existing models where the estimation error is about 5%. Experiments are also performed to prove that the proposed OCV model incorporated in the EKF estimator exhibits good reliability and precision under various loading profiles and temperatures.

A model-based adaptive state of charge estimator for a lithium-ion battery using an improved adaptive particle filter

Obtaining accurate parameters, state of charge (SoC) and capacity of a lithium-ion battery is crucial for a battery management system, and establishing a battery model online is complex. In addition, the errors and perturbations of the battery model dramatically increase throughout the battery lifetime, making it more challenging to model the battery online. To overcome these difficulties, this paper provides three contributions: (1) To improve the robustness of the adaptive particle filter algorithm, an error analysis method is added to the traditional adaptive particle swarm algorithm. (2) An online adaptive SoC estimator based on the improved adaptive particle filter is presented; this estimator can eliminate the estimation error due to battery degradation and initial SoC errors. (3) The effectiveness of the proposed method is verified using various initial states of lithium nickel manganese cobalt oxide (NMC) cells and lithium-ion polymer (LiPB) batteries. The experimental analysis shows that the maximum errors are less than 1% for both the voltage and SoC estimations and that the convergence time of the SoC estimation decreased to 120s.

State of charge estimation of LiFePO4 batteries based on online parameter identification

With the research object of LiFePO4 battery, this paper aims to correctly estimate the battery state of charge (SOC) by constructing a comprehensive SOC estimation strategy. Firstly, recursive least square (RLS) algorithm is adopted to realize online parameter identification of the equivalent battery model; and then an elaborate combination of RLS and Unscented Kalman Filter (UKF) is established, thus the battery model parameters used in UKF are actually obtained recursively by RLS; finally, SOC can be estimated by UKF. This strategy has an obvious adaptability due to the adoption of online parameter identification, so it is also called adaptive SOC estimation technique. Experimental results show that sometimes battery model parameters of different cells can be much different even though terminal voltages of these cells are very close or same when they are under resting state, and this inconsistency among LiFePO4 batteries is captured by the RLS-UKF strategy presented in this paper; and of course battery SOC can also be correctly estimated by using the continuously updated model parameters.

Robust and Adaptive Estimation of State of Charge for Lithium-Ion Batteries

The reliable operation of battery management systems depends critically on the accurate estimation of the state of charge (SOC) and characterizing parameters of a battery system. SOC estimation employs models that must be robust against variations in battery cell electrochemical features, aging, and operating conditions. This paper reveals that commonly used SOC estimation schemes are fundamentally flawed in providing the robustness of SOC estimation against model uncertainties. Parameter estimation methodologies and adaptive SOC estimation design are introduced in this paper to enhance SOC estimation accuracy and robustness. By a scrutiny of the impact of parameter variations on SOC estimation accuracy, the SOC–open-circuit-voltage mapping is identified to be the most critical function that must be accurately established. Identification algorithms are introduced, and their convergence properties are established. The integration of the identification algorithms and SOC estimation schemes lead to an adaptive SOC estimation framework that is superior over the existing methods in providing much improved accuracy and robustness. Experimental studies are conducted to validate the algorithms.

Real-time estimation of battery state-of-charge with unscented Kalman filter and RTOS μCOS-II platform

To develop an advanced battery estimation unit for electric vehicles application, the state-of-charge (SoC) estimation is proposed with an unscented Kalman filter (UKF) and realized with the RTOS μCOS-II platform. Kalman filters are broadly used to deploy various battery SoC estimators recently. Herein, an UKF algorithm has been employed to develop a systematic adaptive SoC estimation framework. Compared with traditional used extended Kalman filter, it uses an unscented transform to deal with the state estimation problem, thus it has the potential to achieve third order accuracy of the Taylor expansion for tracking posterior estimate of the inner inhabited state. Beneficial from it, the SoC estimation accuracy has been improved with higher tracking accuracy and faster convergence ability. To further evaluate and verify the performance of the proposed online SoC estimation approach, a battery-in-loop platform is built and the SoC estimation is calculated with a RTOS μCOS-II platform. The analog acquisition, communication system and SoC estimation algorithms were programmed, the performance of the proposed SoC estimation with UKF algorithm was finally investigated. The battery management system with UKF algorithm and RTOS μCOS-II platform has good performance and it can apply for electric vehicles.

State of charge estimation for lithium-ion batteries: An adaptive approach

State of charge (SoC) estimation is of key importance in the design of battery management systems. An adaptive SoC estimator, which is named AdaptSoC, is developed in this paper. It is able to estimate the SoC in real time when the model parameters are unknown, via joint state (SoC) and parameter estimation. The AdaptSoC algorithm is designed on the basis of three procedures. First, a reduced-complexity battery model in state-space form is developed from the well-known single particle model (SPM). Then a joint local observability/identifiability analysis of the SoC and the unknown model parameters is performed. Finally, the SoC is estimated simultaneously with the parameters using the iterated extended Kalman filter (IEKF). Simulation and experimental results exhibit the effectiveness of the AdaptSoC.