State Of Charge Estimation Model Research Articles

Multi-temperature capable enhanced bidirectional long short term memory-multilayer perceptron hybrid model for lithium-ion battery SOC estimation

In this study, we propose a novel hybrid modeling framework for State of Charge (SOC) estimation across a broad temperature spectrum. First, we build a hybrid model to optimize stacked layers of stacked bidirectional long short term memory networks by introducing dropout mechanisms. At the same time, we also optimize the traditional multi-layer perceptron model to ResMLP, which is improved by introducing residual linkage, and then integrate the two optimization models. Finally, the synergistic effect and attention mechanism of genetic algorithm and particle swarm optimization are used to optimize its parameters. We then rigorously tested the model on nine datasets, including HPPC, DST and BBDST, at different temperatures of 5 °C, 15 °C and 35 °C. Using MAE, RMSE and MAXE benchmarks, our research results show that the proposed hybrid model outperforms the benchmark algorithm, achieving significantly enhanced performance and higher accuracy, and the maximum SOC estimation error is kept below 4.53 %. In addition, experimental evaluation at different temperatures shows the robustness and adaptability of the proposed algorithm.

Estimation of SOC for Li-ion battery-powered three-wheeled electric vehicle using machine learning methods

Abstract The Battery Management System (BMS) serves as the heart of the electric vehicle system, in which estimating the state of charge (SOC) is the crucial part of the BMS to ensure the durability, reliability, and sustainability of the battery pack. Due to its nonlinear characteristics, accurately estimating the SOC for a slow degradation of the charge is highly cumbersome. The literature provides a series of machine learning algorithms (MLA) to estimate and predict the SOC of lithium-ion (Li-ion) battery systems for electric vehicle (EV) applications. The literature has proposed various MLA, coulomb counting, and different Kalman filter methods to address this challenge and estimate the SOC of Li-ion battery systems for EV applications. This research looks at the differences and similarities between the coulomb counting method, the unscented Kalman filter method, and a number of machine learning algorithms. These include linear regression, polynomial linear regression, support vector regression, decision trees, random forests, artificial neural networks (ANN), and long short-term memory (LSTM). The goal is to assess the MLAs' accuracy in estimating battery SOC. Analyzing model errors optimizes the battery's performance parameter. We identify ANN and LSTM as the two most efficient methods for accurate SOC estimation in an EV-operated BMS system by evaluating the performance indices of the aforementioned machine learning methodologies. Once again, the LSTM model for SOC estimation has proven to be highly accurate in analyzing the discrepancy between the actual and predicted traveling ranges of the designed prototype. We design a MATLAB/SIMULINK EV powertrain by collecting realtime data from the Li-ion battery pack, analyzing the SOC variation data, and using the previously mentioned MLA in the Python platform to estimate the SOC and its accuracy. It highlights the effectiveness of advanced MLAs in improving SOC estimation, thereby enhancing the performance and reliability of EV battery systems.

State of Charge Estimation Method of Energy Storage Battery Based on Multiple Incremental Features

Accurately estimating the state of charge (SOC) is crucial for energy storage battery management systems as it ensures battery performance and extends lifespan. However, existing deep learning-based methods often overlook the dynamic process information during battery charging and discharging, which compromises the accuracy of SOC estimation. To address this limitation, this paper proposes a novel SOC estimation method. First, we employ differential processing on the collected voltage, current, and temperature data to capture dynamic feature changes. Next, all features are normalized to ensure they are on the same scale. Finally, the processed data is divided into sliding windows and input into the TCN-BiLSTM-Attention Net (TBANet) model for SOC estimation. The results show that compared with traditional deep learning based SOC estimation methods, adding incremental features to TBANet improves the estimation accuracy by 15.8%. The average absolute error and root mean square error of the experimental results are 0.72% and 0.91%, respectively. In addition, this approach adopts transfer learning methods to verify the strong adaptability of the proposed method on different datasets, which highlights the robustness of TBANet and its potential for wide applicability in real-world scenarios.

Enhanced energy extraction from wind driven PMSG using digital twin model of battery charging system

The pressing need to meet sustainability and climate objectives has prompted a call for expanding the use of renewable energy sources, improving the intelligence and flexibility of electricity grids, and increasing the adoption of electric vehicles and other electricity-powered products. In light of their numerous benefits, widespread electrification and digital technologies can form the basis of energy and climate policy. This research presents an innovative biased transformer and digital twin battery model to support the wind energy based electric vehicle battery charging system. During periods of low and moderate wind, the biased transformer is utilized to increase the voltage for charging electric vehicles. A digital twin of the battery system creates a window into battery charging and aging levels by evaluating the data gathered based on internal resistance. Furthermore, the State of Charge estimation model and different internal resistance estimation algorithms are also exploited. A novel method for precise State of Charge (SOC) estimation in third-gen battery models is presented, integrating Collaborative Gradient Boosting and Adaptive Extended Kalman Filter (AEKF). This approach, implemented in MATLAB Simulink, combines machine learning and adaptive filtering, enhancing accuracy and adaptability for efficient battery management. The functionalities and resilience of both hardware and software of the proposed system are validated under field operation.

Accurate state-of-charge estimation for sodium-ion batteries based on a low-complexity model with hierarchical learning

Accurate estimation of state-of-charge (SOC) in batteries is of paramount importance for effective and safe battery system management. Sodium-ion batteries' distinctive features on open-circuit voltage and their near-linear relationships with SOC provide a fresh perspective on SOC estimation compared to lithium-ion counterparts. Therefore, this study proposes a low-complexity and wide-adaptability data-driven model for SOC estimation of sodium-ion batteries. Enhanced pulse test across a wide spectrum of conditions is conducted to construct the training set and a hierarchical learning strategy is designed to train the model parameters. To validate this model, tests and evaluations using data of three driving cycles are conducted. The proposed model yields root mean square errors of 0.89 % and 0.63 % for 3.2 Ah and 10 Ah sodium-ion batteries from different manufacturers, respectively. Furthermore, we demonstrate the strong robustness of the model by applying Gaussian noises to the sampled data. Compared to existing data-driven methods for battery SOC estimation, our proposed model achieves remarkably promising performance with significantly lower parameter counts and FLOPs, which is quite attractive in implementation. This work underscores the significant potential of leveraging the distinctive characteristics of sodium-ion batteries to achieve practical and reliable state estimation.

Exploring large language model for generic and robust state-of-charge estimation of Li-ion batteries: A mixed prompt learning method

State-of-charge (SOC) estimation is important to ensure safe functioning of Li-ion batteries (LIBs). However, distinct measurements, harsh temperatures, and dynamic operations pose challenges in estimating intricate SOC changes of multiple LIBs with one estimator. Hence, this paper proposes a novel mixed prompt learning method to explore a large-scale pretrained language model (PLM) for SOC estimation. A new hard prompt generator is proposed to translate LIB data into instruction and answer text, eliciting the inherent representational capability of PLM to jointly learn the sequential patterns and contextual semantics of measurements through language modeling for accurate SOC estimation. A new soft prompt adapter is proposed to encode task-specific information of different LIBs into a small set of independent vectors, ensuring PLM adaptation with minimal parameters while maintaining good generalization. By integrating soft prompt vectors along the forward propagation, the hidden states of PLM are dynamically regulated to characterize volatile and variable SOC for robust estimation. Extensive experiments show that by leveraging mixed hard-soft prompts, PLM can make accurate, generic, and robust estimates for multiple LIBs simultaneously in subzero temperature, charge-pause-discharge, and low-capacity discharge scenarios, with the average MAE, RMSE, and MAX of all tasks as low as 1.20 %, 1.51 %, and 5.29 %, respectively.

SVM-assisted ANN model with principal component analysis based dimensionality reduction for enhancing state-of-charge estimation in LiFePO4 batteries

Accurate estimation of state-of-charge (SoC) is significant for monitoring the operation of LiFePO4 batteries. This paper addresses the challenges posed by the nonlinear characteristics of LiFePO4 batteries, which adversely affect the accuracy of SoC estimation. The proposed novel methodology for SoC estimation in LiFePO4 batteries involves a Support Vector Machine (SVM) assisted Artificial Neural Network (ANN) model incorporating principal component analysis (PCA) to efficiently interpret the input data. To improve the prediction accuracy, the non-linear characteristics of LiFePO4 are divided into three parts and each of these parts is used to train a separate ANN model. Further, an optimal number of hidden layers and neurons are selected for each ANN model to minimize the prediction errors. The usage of dedicated smaller datasets for each ANN model simplifies the structure. SVM classifies the battery operating regions and selects the most suitable ANN model for SoC estimation. PCA is applied to process the obtained experimental data resulting in three principal components serving as inputs for the SVM-assisted ANN model. Further, with PCA the input dimensions are reduced from four to three, thereby leading to computational simplicity. The input data comprises of current, voltage, open-circuit voltage and temperature of the battery. An experimental prototype, comprising a customized battery pack and sensing mechanisms, is developed for data collection for training SVM and ANN models. With the proposed SVM-assisted ANN involving PCA, the loss function is minimized and an average Root Mean Square Error (RMSE) of 0.3133 is achieved. This demonstrates the feasibility, accuracy and applicability of SoC estimation with the developed SVM-assisted ANN model for LiFePO4 batteries.

Efficient estimation of state of charge of lithium-ion batteries

The promotion of electric vehicles can help reduce carbon emissions and mitigate the greenhouse effect. Lithium-ion batteries are one of the main power sources for electric vehicles, whose state of charge is a key parameter of the battery management system to ensure the safe operation of electric vehicles. The complex structure of the battery makes the state of charge unable to be directly measured, so this paper establishes a mathematical model to estimate the state of charge based on four parameters (voltage, current, wavelength and light intensity), aiming to provide a high-precision model for state of charge measurement and establish a mathematical model which can help guide actual production. These four parameters can be measured by voltmeters, ammeters, and optical fibers. In this paper, the least squares method is used to perform global linear regression and global quadratic regression of experimental data, and a data pre-treatment is proposed to improve the behavior of the linear equation system. Also, the ridge regression method is used to achieve an effective solution of the ill-conditioned linear equation system. Then, the piecewise linear regression is introduced to optimize the global regression model, and effectively reduces the regression error by capturing the local features of the data. In order to meet the actual engineering requirements, constraints satisfying segmental continuity are added in the piecewise linear regression model. Finally, the regression results are compared with the results obtained by the Machine Learning method. Besides, the proposed methods outperform the Machine Learning method with a sufficient number of segments. The state of charge estimation model established in this paper has high approximation accuracy, strong interpretability, low operational complexity, and has certain engineering application value.

Extreme learning machine model with honey badger algorithm based state-of-charge estimation of lithium-ion battery

Accurate state-of-charge (SOC) detection was still a challenging task to complete due to complex battery dynamics and constantly changing external conditions. The formula for SOC was difficult to determine since external parameters including voltage, current, temperature, and battery arrangement were complex. Also the methods for estimating SOC that were already in use were not always appropriate for the same car operating in various road and climatic conditions. In all situations, the conventional methodologies did not deliver an accurate estimation performance. Here, a unique optimization-based Extreme Learning Machine (ELM) was created to accurately determine a battery's SOC and enhance the operation and safety of battery systems. A lithium ion battery was first created, and data on its current, voltage, SOC, capacity, duration, and discharge rate were gathered to produce a real-time dataset at several temperatures, including 00,250 and 450. The dataset underwent additional pre-processing to standardize the values and enhance the accuracy of the data. To determine the precise state of the battery, these pre-data were loaded into the ELM model. However, the performance of ELM was significantly influenced by the length of training and the number of neurons in a hidden layer. An advanced Honey Badger Optimization Algorithm (HBA) was used to choose the appropriate hidden neurons and increase the estimation accuracy in order to overcome this problem. The proposed SOC estimation model provides 97% accuracy in the FUDS drive cycle and 99% accuracy in the US06 drive cycle. The proposed model provides a well performance for estimating SOC in lithium-ion battery at various temperature, also the proposed model was fit for real time implementation.

A key-term separation based least square method for Hammerstein SOC estimation model

In this paper, a Hammerstein state of charge (SOC) estimation model for lithium-ion batteries with two inputs and single output is constructed to map the relation between battery SOC and its discharge current/voltage, and a key-term separation based least square (KT-LS) algorithm is studied to identify the model parameters so as to identify the battery SOC. The thought is, by adopting the key-term separation principle, to decompose the key-term from the linear element and to substitute the expression of the nonlinear element only into the decomposed key-term, thus to express the model output as a linear auto-regression form about parameters. Then the least square algorithm is performed to optimize parameters in the reformed auto-regression form of the Hammerstein SOC system. The advantages of the explored the KT-LS algorithm contains the least parameters required, thus the calculation burden of the KT-LS algorithm is small compared with the over-parameterized model based algorithm. In the simulation experiment part, the performance of the KT-LS algorithm under different conditions are analyzed under UDDS and LA92 conditions.; the performance comparison between the KT-LS algorithm and the key-term separation based stochastic gradient (KT-SG) algorithm is carried out; the performance of the KT-LS algorithm based Hammerstein model method is compared with that of the back propagation (BP) neural network, the Long Short Term Memory (LSTM) neural network and the Extended Kalman filter (EKF) method. The simulation results show that the KT-LS algorithm based Hammerstein SOC model can effectively estimate the SOC of lithium-ion batteries.

Investigation of denoising autoencoder-based deep learning model in noise-riding experimental data for reliable state-of-charge estimation

State-of-charge (SOC) estimation plays a crucial role in battery management systems to ensure safe and reliable operation. However, SOC estimation remains challenging due to the dynamic nature of battery systems and varying ambient conditions. Data-driven methods have emerged as effective tools for analyzing nonlinear dynamical systems, but their performance heavily relies on data quality. In actual applications, data susceptible to distortions caused by external factors such as sensor failure, circuitry, and temperature variations, leading to degraded model performance. To address the performance degradation resulting from data quality deterioration, this paper introduces a denoising autoencoder is implemented as a stacked multi-layer perceptron, which learns to reconstruct distorted data. Furthermore, we propose the ensemble method that combines the autoencoder with an estimation model for SOC estimation in lithium-ion batteries. The effectiveness of the proposed model is demonstrated through tests conducted on a dataset comprising drive cycle profile of Panasonic 18650PF cells. The model validated under two ambient temperatures scenarios: identical and different, using a distorted dataset with added randomly added noise and dropout. The experimental results reveal that the proposed model achieved a 3 % error in training the drive profile relative to the actual values at different ambient temperatures. When compared to the plain model, the proposed ensemble model showed an increased RMSE of 4 %. Additionally, the performance of different estimation models was compared, with the LSTM model achieving an RMSE 0.67 at different ambient temperatures, outperforming the Support Vector Regression (SVR) with an RMSE 1.35 and the Extended Kalman Filter (EKF) with an RMSE of 0.87.

A novel RBFNN-UKF-based SOC estimator for automatic underwater vehicles considering a temperature compensation strategy

Accurate state of charge (SOC) estimation of batteries is a prerequisite for the reliable operation of automatic underwater vehicles. Currently, the accuracy of traditional SOC evaluation algorithms deteriorates significantly at low temperatures and low SOCs. Hence, a novel SOC estimator is proposed in this study, consisting of three efforts. Firstly, a new radial basis function neural network (RBFNN) battery model is built to replace the equivalent circuit model (ECM) for SOC estimation. Then, based on the relation between SOC and terminal voltage at a different temperature, a temperature compensation strategy is developed, which is an effortless operation and does not increase the computational burden. Finally, incorporating the new battery model, the temperature compensation strategy, and the unscented Kalman filter (UKF), a novel SOC estimation frame expressed as RBFNN-UKF is designed.The performance of the proposed method, including accuracy, generalization ability, and low-temperature adaptation, is evaluated systematically based on a publicly available dataset, where the inaccurate initial value and the current errors are added in each case. The results show that: (1) The SOC estimation curve of RBFNN-UKF can converge quickly to the reference curve and maintain good consistency even at low SOCs; (2) The proposed method exhibits excellent generalization capability for different dynamic cycles; (3) At low temperatures, the SOC estimation error of the RBFNN-UKF is reduced to 17 % of traditional ECM-UKF algorithm with the recursive least squares parameter identification method. The above results indicate that the proposed RBFNN-UKF-based SOC estimator has a high application value for AUVs and other vehicles working in complex environments.

State of Charge Estimation for Lithium-Ion Battery Based on Unscented Kalman Filter and Long Short-Term Memory Neural Network

State of charge (SOC) estimation is the core algorithm of the battery management system. However, the commonly used model-based, data-driven, or experiment-based methods struggle to independently achieve accurate SOC estimation under different working conditions and temperatures, which affects battery performance and safety. To this end, this paper proposes an online SOC estimation method that combines the model-driven and double-data-driven approaches. The unscented Kalman filter (UKF) based on the first-order RC model is used to achieve robust SOC estimation, while the data-driven long short-term memory (LSTM) neural network is used to achieve fast SOC estimation. The former model has an excellent dynamic performance and the latter has high steady-state accuracy. The SOC estimation results are input into the SOC estimation model of series LSTM so that the stable but inaccurate SOC values estimated by UKF in the first part and the accurate but fluctuating SOC values estimated by LSTM can be correlated and corrected, achieving a fast and accurate SOC estimation under various working conditions. The estimation results show that the above method has strong robustness and high accuracy, and effectively reduces model complexity and data redundancy. In addition, the root mean square error of SOC estimation under different working conditions is controlled within 1–2.3% at 0 °C, 25 °C, and 45 °C, which is better than the traditional single-SOC estimation method.

Improved Feature Decoupling Transfer Network Modeling based on Singular Value Decomposition for SOC Estimation in Energy-Storage Lithium-ion Batteries

Deep learning (DL) methods is applied extensively in the field of state of charge (SOC) estimation, which require training data and test data to have similar distribution. Discrepancies in data distribution arising from the complexity and diversity of lithium-ion batteries under operational conditions in practice, as well as the difficulty in obtaining data labels, make it enormously challenging to access sufficient battery data to train a specific deep estimator. Aiming to improve the performance of cross-domain SOC estimation for lithium-ion batteries, a model for SOC estimation which combines transfer learning with singular value decomposition (SVD) is proposed. To begin with, a gated recurrent unit (GRU) network is employed to avail the nonlinear dynamic characteristics of the battery from the source and target domains. Then, the features are decoupled by using SVD method to extract task-relevant, important and minor information in the network. Further, the amount of transferred information over the source network to the target network is automatically tuned by the maximum mean discrepancy (MMD) to determine the different degrees of similarity in domain, and the cosine discrepancy to measure the discrepancy on the same domain, which achieves the optimized performance of the target network.

State of charge estimation for lithium-ion batteries based on cross-domain transfer learning with feedback mechanism

When the deep learning model is applied to estimate battery state of charge (SOC), the information inside the training set cannot be leveraged thoroughly, which would cause poor SOC estimation accuracy and robustness on the testing set. To solve the problem, this paper proposes an adaptive convolutional neural network-gated recurrent unit with Kalman filter and feedback mechanism (Fb-Ada-CNN-GRU-KF) for SOC estimation considering distribution difference of data segments inside the training set through transfer learning and extracting the spatial information through convolutional layer. Furthermore, the feedback mechanism provides the model more information to learn to correct the systematic error, and the KF in the proposed model works as a post data processor to obtain a steady and smooth SOC estimation results. Experimental and comparison results show that the proposed model for SOC estimation outperforms the existing deep learning methods in terms of the accuracy, generalization and stability.

Small Dataset-Based Closed-Loop State of Charge Estimation for Pure Electric Construction Machinery With Large Sensor Error: A Case Study of 5-ton Loader

Pure electric construction machinery (PECM) is the future development trend for construction machinery. Compared with other electric drive systems, the PECM systems are often accompanied by complex working conditions, frequent high current pulse signals, limited memory sources, and heavier sensor noise. To improve the robustness and accuracy of state of charge (SOC) estimation for the PECM using small dataset with large sensor error, a hybrid approach combined machine learning method with physical method is proposed in this paper. Firstly, the Gaussian process regression (GPR) is employed to train an open-loop SOC estimation model with a simple moving window method. Secondly, a framework of hybrid SOC estimation is proposed based on an improved version of the Kalman filter to improve the robustness of the GPR model with large sensor error. Finally, a series of experiments are carried out to evaluate the proposed approach considering temperature variation, measurement drift noise, and users’ habits. It is worth noting that the sampling frequency of training data is only 0.1 Hz. The proposed approach is compared with the most widely used machine learning methods, which verifies the high accuracy and strong robustness of the proposed approach.

ANN-based State of Charge Estimation of Li-ion Batteries for Embedded Applications

The conventional state of charge (SOC) estimation model has several concerns, such as accuracy and reliability. In order to realize robust SOC estimation for embedded applications, this study focuses on three concerns of the existing SOC estimation model: accuracy, robustness, and practicality. In improving the estimation accuracy and robustness, this study took into account the dynamic of the actual SOC caused by the dynamic charging and discharging process. In practice, the charging and discharging processes have characteristics that must be considered to realize robust SOC estimation. The model-based SOC estimation developed based on the virtual battery model causes difficulties for real-time applications. Additionally, model-based SOC estimation cannot be reliably extrapolated to different battery types. In defining the behavior of various types of batteries, the model-based SOC estimation must be updated. Hence, this study utilized data-driven SOC estimation based on an artificial neural network (ANN) and measurable battery data. The ANN model, which has excellent adaptability to nonlinear systems, is utilized to increase accuracy. Additionally, using measurable battery data such as voltage and current signals, the SOC estimation model is suitable for embedded applications. Results indicate that estimating SOC with the proposed model reduced errors with respect to actual datasets. In order to verify the feasibility of the proposed model, an online estimation was out on the embedded system with the use of C2000 real-time microcontrollers. Results show that the proposed model can be executed in an embedded system using measurable battery data.

State of Charge Estimation for Batteries Based on Common Feature Extraction and Transfer Learning

The state of charge (SOC) of a battery is a key parameter of electrical vehicles (EVs). However, limited by the lack of computing resources, the SOC estimation strategy used in vehicle-mounted battery management systems (V-BMS) is usually simplified. With the development of the new energy vehicle big data platforms, it is possible to obtain the battery SOC through cloud-based BMS (C-BMS). In this paper, a battery SOC estimation method based on common feature extraction and transfer learning is proposed for C-BMS applications. Considering the diversity of driving cycles, a common feature extraction method combining empirical mode decomposition (EMD) and a compensation strategy for C-BMS is designed. The selected features are treated as the new inputs of the SOC estimation model to improve the generalization ability. Subsequently, a long short-term memory (LSTM) recurrent neural network is used to construct a basic model for battery SOC estimation. A parameter-based transfer learning method and an adaptive weighting strategy are used to obtain the C-BMS battery SOC estimation model. Finally, the SOC estimation method is validated on laboratory datasets and cloud platform datasets. The maximum root-mean-square error (RMSE) of battery SOC estimation with the laboratory dataset is 2.2%. The maximum RMSE of battery pack SOC estimation on two different electric vehicles is 1.3%.

State-of-charge estimation of lithium-ion batteries based on ultrasonic detection

In order to characterize the state of charge of the lithium battery from the internal material properties of the lithium battery, this paper proposes a method of estimating the state of charge of the lithium battery based on ultrasonic non-destructive testing. First, this paper uses the ultrasonic flaw detector and other equipment to obtain the feedback signal of ultrasonic detection, then introduces the empirical mode decomposition (EMD) algorithm to eliminate the interference present in the ultrasonic feedback signal, and reconstructs the decomposed ultrasonic feedback signal to improve the continuity of the ultrasonic signal. Secondly, the Hilbert transform is performed on the ultrasonic signal. The maximum instantaneous energy of the ultrasonic signal is extracted with the ultrasonic energy entropy and the ultrasonic reception entropy as the characteristic quantity to measure the charge state of the lithium battery. Finally, this paper uses relevance vector regression to build a lithium battery state of charge estimation model. The experiments show that the method proposed in the thesis is practical and feasible, and has good estimation accuracy. The acoustic characteristics proposed in this paper provide a certain reference for subsequent related research.

Recursive ARMAX-Based Global Battery SOC Estimation Model Design using Kalman Filter with Optimized Parameters by Radial Movement Optimization Method

Precise estimating battery state-of-charge (SOC) is an important factor in determining vehicle range in an electric or hybrid vehicle. However, the parameters of battery are highly dependent on environmental conditions such as temperature. One of the main drawbacks in battery SOC estimation methods by using existing approaches is inability to adapt to the variable environmental operating conditions. In this study, a hybrid technique which combines the Kalman filter and recursive autoregressive exogeneous moving average model is proposed for the online battery parameters estimation. To design robust SOC estimation to varying battery parameters, the parameters of Kalman filter are optimized with the radial movement optimization metaheuristic algorithm. The proposed approach is implemented considering both different temperatures (0 °C, 25 °C, and 40 °C) and driving test cycles, UDDS, LA-92, and US06. Second-order RC battery equivalent model-based approach are compared with the proposed method, and the result shows that the proposed method is better than the conventional method in the aspects of average statistical parameters for all the driving test cycles.