State Of Charge Estimation Approach Research Articles

Estimation of Lithium Battery State of Charge Using the LTG-SABO-GRU Model

Abstract Accurate estimation of the state of charge (SOC) in lithium batteries is crucial for optimizing energy utilization and ensuring battery safety within Battery Management Systems (BMS). While deep learning techniques have made significant progress, time-series models based on the Gate Recurrent Unit (GRU) have gained widespread application in SOC estimation. However, their performance heavily hinges on the initial hyperparameter settings, impacting both precision and application range. To address this challenge, we propose a novel algorithm—the Logistic-tent-Gold Subtraction Average-based Optimizer (LTG-SABO)—which combines composite chaotic mapping with the golden sine algorithm. The LTG-SABO algorithm aims to optimize key hyperparameters of the GRU model, thereby enhancing precision and robustness in SOC estimation. By leveraging the Logistic-tent composite chaotic mapping for population initialization, our approach not only expands the search space but also effectively prevents algorithm convergence to local optima. Additionally, integrating the Gold-SA strategy further enhances the global search capability of the SABO algorithm, significantly reducing convergence time. The computational results reveal that the proposed LTG-SABO-GRU model outperforms the traditional GRU model in estimating SOC precision under both normal and extreme temperature conditions. Specifically, the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) show a substantial improvement, increasing by over 50% compared to the traditional model. Moreover, the LTG-SABO-GRU model exhibits significantly fewer convergence iterations than existing typical population optimization algorithms. This study introduces a novel, efficient, and practical approach for SOC estimation in BMS applications.

A modeling and state of charge estimation approach to lithium-ion batteries based on the state-dependent autoregressive model with exogenous inputs

Dynamic modeling and state of charge (SOC) estimation of lithium-ion batteries (LIBs) is a critical technology in the battery management system. Aiming at the essential nonlinear characteristics of LIBs and the time-varying operating state caused by the influence of the external environment including load changes and other factors, this paper proposes to adopt the state-dependent autoregressive model with exogenous inputs (SD-ARX) to describe its nonlinear dynamic characteristics. This type of model first constructs state signal quantities that can characterize the dynamic properties of LIBs and uses them as inputs to the radial basis function neural network to approximate the functional-type coefficients of the SD-ARX model, which is used to guide the model to represent the nonlinear dynamic properties of LIBs under different operating states. Benefiting from the model can be represented as a linear combination of nonlinear functions, the model parameters identified offline by a structured nonlinear parameter optimization method. Finally, the SOC is estimated online using an adaptive extended Kalman filter based on the established model. The results show that the method can reliably estimate the SOC of a battery under different working conditions and a relatively wide temperature range and achieves a balance between accuracy and real-time performance.

Robust state-of-charge estimation for LiFePO4 batteries under wide varying temperature environments

During the driving process of electric vehicles, the ambient temperature exhibits diverse variations with regional characteristics. To achieve robust state of charge (SOC) estimation for lithium-ion batteries under various varying temperature environments, this paper proposes an enhanced model-based closed-loop SOC estimation approach. First, beginning with a mechanistic analysis of batteries, the traditional second-order equivalent circuit model is enhanced by incorporating critical solid-phase diffusion effects during battery operation. Furthermore, utilizing data collected from multiple constant temperature environments, the complete enhanced battery model that accounts for the influence of current rates across a wide temperature range is constructed. Subsequently, under environments of different varying temperature settings, we design a series of complex operation experiments to verify the accuracy and generalizability of the established battery model. Meanwhile, a high-performance adaptive diagonalization of matrix cubature Kalman filter is introduced to address the challenge of fluctuating sampling noises in battery operation. Finally, the robustness and generalization of the proposed SOC estimation method are verified in multiple complex operating experiments under varying temperatures with non-Gaussian noise interferences and with non-full charging schemes. Remarkably, the proposed approach consistently delivers high-precision SOC estimation results across all scenarios, maintaining root mean square error and mean absolute error below 1.5%.

ICNCS: Internal Cascaded Neuromorphic Computing System for Fast Electric Vehicle State-of-Charge Estimation

Accuracy and speed of Lithium-ion battery state of charge (SOC) estimation determine the reliability and stability of electric vehicle (EV), as well as promoting the development of smart home energy management system. Existing SOC estimation approaches embedded in commercial EVs still suffer from limitations of low precision, effectiveness, and relatively low robustness. To address these issues, we propose an internal cascaded neuromorphic computing system (ICNCS) via memristor circuits for EV SOC estimation. Specifically, we use three circuit modules to facilitate the design of the proposed ICNCS. Firstly, a bidirectional gated recurrent unit (Bi-GRU) circuit module is designed, enabling adequate feature extraction from the time-contextual battery information. Secondly, an attention circuit module is proposed to distinguish the useful and unimportant information related to SOC estimation. Thirdly, the Kalman filter module is constructed to eliminate the random noise caused by data transmission and processing. Finally, a series of experiments and analysis demonstrate that the proposed ICNCS has good performances in terms of accuracy (the lowest achievable RMSE and MAE are 0.853 and 0.711, respectively), time efficiency (approximately 16 20 times), and robustness (anti-noise capacity), indicating an advancement in consumer electronics applications.

Lithium-ion battery expansion mechanism and Gaussian process regression based state of charge estimation with expansion characteristics

Lithium-ion battery (LIB) thickness variation due to its expansion behaviors during cycling significantly affects battery performance, lifespan, and safety. This study establishes a three-dimensional electrochemical-thermal-mechanical coupling model to investigate the impacts of thermal expansion and particle intercalation on LIB thickness variation, respectively. Results indicate that thickness variation induced by particle intercalation predominantly determines LIB expansion behavior, contributing to 92 % of the observed thickness variation. Moreover, the expansion behavior of LIBs across the entire state of charge (SOC) ranges can be categorized into four stages based on the expansion rate, with turning points closely correlating with the positions of peaks in the Incremental Capacity (IC) curve. This phenomenon underscores the nuanced relationship between LIB thickness variation characteristics and SOC. Consequently, this study proposes a novel SOC estimation approach based on Gaussian regression processes utilizing expansion behavior and voltage characteristics. The experimental results indicate that the maximum error does not exceed 0.0076, and the root mean square error (RMSE) remains within 0.0018 for the constant charging/discharging conditions under different current rates. This research provides guidance for expansion mechanism investigation and SOC estimation optimization.

State of Charge Estimation for Electric Vehicles Using Random Forest

This paper introduces an innovative approach to addressing a critical challenge in the electric vehicle (EV) industry—the accurate estimation of the state of charge (SOC) of EV batteries under real-world operating conditions. The electric mobility landscape is rapidly evolving, demanding more precise SOC estimation methods to improve range prediction accuracy and battery management. This study applies a Random Forest (RF) machine learning algorithm to improve SOC estimation. Traditionally, SOC estimation has posed a formidable challenge, particularly in capturing the complex dependencies between various parameters and SOC values during dynamic driving conditions. Previous methods, including the Extreme Learning Machine (ELM), have exhibited limitations in providing the accuracy and robustness required for practical EV applications. In contrast, this research introduces the RF model, for SOC estimation approach that excels in real-world scenarios. By leveraging decision trees and ensemble learning, the RF model forms resilient relationships between input parameters, such as voltage, current, ambient temperature, and battery temperatures, and SOC values. This unique approach empowers the model to deliver precise and consistent SOC estimates across diverse driving conditions. Comprehensive comparative analyses showcase the superiority of the RF over ELM. The RF model not only outperforms in accuracy but also demonstrates exceptional robustness and reliability, addressing the pressing needs of the EV industry. The results of this study not only underscore the potential of RF in advancing electric mobility but also suggest a promising integration of the SOC estimation approach into the battery management system of BMW i3. This integration holds the key to more efficient and dependable electric vehicle operations, marking a significant milestone in the ongoing evolution of EV technology. Importantly, the RF model demonstrates a lower Root Mean Squared Error (RMSE) of 5.9028% compared to 6.3127% for ELM, and a lower Mean Absolute Error (MAE) of 4.4321% versus 5.1112% for ELM across rigorous k-fold cross-validation testing, reaffirming its superiority in quantitative SOC estimation.

A review of battery state of charge estimation and management systems: Models and future prospective

AbstractBatteries are considered critical elements in most applications nowadays due to their power and energy density features. However, uncontrolled charging and discharging will negatively affect their functions and might result in a catastrophic failure of their applications. Hence, a battery management system (BMS) is mandated for their proper operation. One of the critical elements of any BMS is the state of charge (SoC) estimation process, which highly determines the needed action to maintain the battery's health and efficiency. Several methods were used to estimate the Lithium‐ion batteries (LIBs) SoC, depending on the LIBs model or any other suitable technique. This article provides a critical review of the existing SoC estimation approaches and the main LIB models with their pros and cons, their possibility to integrate with each other's for precise estimation results, and the applicability of these techniques in electric vehicles and utility applications with the commonly used standards and codes in these sectors. Moreover, this study will also explore a future framework for integrating digital twins (DTs) with BMSs for improved and advanced management. Based on this comprehensive review, it can be concluded that merging the model‐based estimation techniques with the data‐driven approaches with their promising development to determine the dynamic patterns inside the battery can efficiently achieve precise estimation results while reducing the complexity of these models. This integration will align also with the integration of digital twin technology to provide complete and accurate supervision for the BMSs.This article is categorized under: Emerging Technologies > Energy Storage Emerging Technologies > Digitalization Energy and Power Systems > Distributed Generation

A time-series Wasserstein GAN method for state-of-charge estimation of lithium-ion batteries

Estimating the state-of-charge (SOC) of lithium-ion batteries is essential for maintaining secure and reliable battery operation while minimizing long-term service and maintenance expenses. In this work, we present a novel Time-Series Wasserstein Generative Adversarial Network (TS-WGAN) approach for SOC estimation of lithium-ion batteries, characterized by a well-designed data preprocessing process and a distinctive WGAN-GP architecture. In the data preprocessing stage, we employ the Pearson correlation coefficient (PCC) to identify strongly associated features and apply feature scaling techniques for data normalization. Moreover, we leverage polynomial regression to expand the original features and utilize principal component analysis (PCA) to reduce the computational load and retain essential information by projecting features into a lower-dimensional subspace. Within the WGAN-GP architecture, we originally devise a Transformer as the generator and a Convolution Neural Network (CNN) as the critic to make the most of local (CNN) and global (Transformer) variables. The overall model is trained with the WGAN, incorporating gradient penalty loss for training purposes. Simulation outcomes using real-road dataset and laboratory dataset reveal that TS-WGAN surpasses all baseline methods with enhanced accuracy, stability, and robustness. The coefficient of determination (R2) for both datasets exceeds 99.50%, demonstrating its potential for practical application.

MDGN: Circuit design of memristor‐based denoising autoencoder and gated recurrent unit network for lithium‐ion battery state of charge estimation

AbstractDue to the highly complex and non‐linear physical dynamics of lithium‐ion batteries, it is unfeasible to measure the state of charge (SOC) directly. Designing systems capable of accurate SOC estimation has become a key technology for battery management systems (BMS). Existing mainstream SOC estimation approaches still suffer from the limitations of low efficiency and high‐power consumption, owing to the great number of samples required for training. To address these gaps, this paper proposes a memristor‐based denoising autoencoder and gated recurrent unit network (MDGN) for fast and accurate SOC estimation of lithium‐ion batteries. Specifically, the DAE circuit module is designed to extract useful feature representation with strong generalization and noise immunity. Then, the gated recurrent unit (GRU) circuit module is designed to learn the long‐term dependencies between high‐dimensional input and output data. The overall performance is evaluated by root mean square error (RMSE) and mean absolute error (MAE) at 0, 25, and 45°C, respectively. Compared with the current state‐of‐the‐art methods, the entire scheme shows its superior performance in accuracy, robustness, and operation cost (referring to time cost).

A novel lithium-ion battery state of charge estimation method based on the fusion of neural network and equivalent circuit models

Accurate estimating the state of charge (SOC) can improve battery reliability, safety, and extend battery service life. The existing battery models used for SOC estimation inadequately capture the dynamic characteristics of a battery in a wide temperature over the full SOC range, leading to significant inaccuracies in SOC estimation, especially in low temperature and low SOC. A novel SOC estimation approach is developed based on a fusion of neural network model and equivalent circuit model. Firstly, the weight-SOC-temperature relationship is established by obtaining the weights of the equivalent circuit model and the neural network model offline using the standard deviation weight assignment method. Following that, an online adaptive weight correction approach is implemented to update the weight-SOC-temperature relationship. Finally, a novel multi-algorithm fusion technique is utilized to achieve SOC estimation accuracy within 1%. The results clearly demonstrate that the developed approach achieves twice the accuracy of the existing approach, highlighting its superior effectiveness.

Battery SOC estimation from EIS data based on machine learning and equivalent circuit model

Estimating the state of charge (SOC) of batteries is fundamental for the proper management and safe operation of numerous systems, including electric vehicles, smart energy grids, and portable electronics. While there is no practical method for direct measurement of SOC, several estimation approaches have been developed, including a growing number of machine-learning-based techniques. Machine learning methods are intrinsically data-driven but can also benefit from a-priori knowledge embedded in a model. In this work, we first demonstrate, through exploratory data analysis, that it is possible to discriminate between different SOC from electrochemical impedance spectroscopy (EIS) measurements. Then we propose a SOC estimation approach based on EIS and an equivalent circuit model to provide a compact way to describe the frequency domain and time-domain behavior of the impedance of a battery. We experimentally validated this approach by applying it to a dataset consisting of EIS measurements performed on four lithium-ion cylindrical cells at different SOC values. The proposed approach allows for very efficient model training and produces a low-dimensional SOC classification model that achieves above 93% accuracy. The resulting low-dimensional classification model is suitable for embedding into battery-powered systems and for online SOC estimation.

Hybrid deep learning model for efficient state of charge estimation of Li-ion batteries in electric vehicles

State of charge (SoC) estimation is critical for the safe and efficient operation of electric vehicles (EVs). This work proposes a hybrid multi-layer deep neural network (HMDNN)-based approach for SoC estimation in EVs. This HMDNN uses Mountain Gazelle Optimizer (MGO) as a training algorithm for the deep neural network. Our method leverages the intrinsic relationship between the SoC and the voltage/current measurements of the EV battery to accurately estimate the SoC in real time. We evaluate our approach on a large dataset of real-world EV charging data and demonstrate its effectiveness in comparison to traditional SoC estimation methods. Four diverse Li-ion battery datasets of electric vehicles are employed which are the dynamic stress test (DST), Beijing dynamic stress test (BJDST), federal urban driving schedule (FUDS), and highway driving schedule (US06) with different temperatures of 0oC,25oC,45oC. The comparison is made with Mayfly Optimization Algorithm based DNN, Particle Swarm Optimization based DNN and Back-Propagation based DNN. The evaluation indices used are normalized mean square error (NMSE), root mean square error (RMSE), mean absolute error (MAE), and relative error (RE). The proposed algorithm achieves 0.1% NMSE and 0.3% RMSE on average on all datasets, which validates the effective performance of the proposed model. The results show that the proposed neural network-based approach can achieve higher accuracy and faster convergence than existing methods. This can enable more efficient EV operation and improved battery life.

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.

Mechanics-based state of charge estimation for lithium-ion pouch battery using deep learning technique

Accurate state of charge (SOC) estimation helps achieve efficient battery management, which is essential for transportation electrification. Significantly different from existing data-driven estimation methods only considering battery electrical information, this study proposes a mechanics-based battery SOC estimation using deep learning techniques. First, an experimental setup for measuring pouch-type battery stress is designed, followed by constructing four typical operating conditions to establish a sophisticated battery dataset and investigate the primary relationship between battery stress and SOC. Then, a data-driven estimation model composed of long short-term memory neural network is investigated to achieve the interlink between battery external measurements and internal states, in which the battery voltage, current, and stress sequences within a sliding window length are fed into the deep learning model. Quantitative experimental results demonstrate that the proposed mechanics-based battery SOC estimation approach can achieve acceptable accuracy and is adaptable to different training and operating conditions, as well as ensure the estimation performance under limited data length. Moreover, the proposed method has also been proven robust to the interference of battery measurement noise compared to the traditional estimation method.

A novel combined online method for SOC estimation of a Li-Ion battery with practical and industrial considerations

Estimation of the state of charge (SOC) in the battery management systems (BMS) is very crucial. However, the BMS consistently suffers from inaccuracy of SOC estimation and high computational burden in industrial applications. Herein, we propose a novel combined SOC estimation approach with high accuracy, simplicity in implementation and, robustness that can be implemented on the low-cost microcontrollers. The basis of the method is to online identification the open circuit voltage (OCV) value of the battery simultaneously with other unknown parameters of the battery equivalent circuit model (ECM). Using this identified OCV, SOC is extracted from the OCV-SOC curve, directly. This direct method is an open-loop estimation method and tends to get lower SOC accuracy compared with known methods. To overcome this disadvantage, a combined method is proposed. Hence, to estimate SOC in this method, in the middle part of the OCV-SOC curve (linear part) and after identifying OCV from recursive least square algorithm (RLS) method with a forgetting factor, SOC is estimated directly via OCV-SOC curve. Furthermore, in the other parts of the curve especially non-linear parts, SOC is estimated with the EKF algorithm. In summary, not only estimation accuracy will increase, but also the computational burden of the EKF will decrease. In this paper, voltage and current samples of the battery at each sample time are the inputs of the algorithms and gained from the known “LA-92 dynamic driving cycle” test. To validate the efficiency of the presented method, results are compared with the EKF algorithm and direct method. The experimental results show that the proposed method reduces the EKF calculations by almost 15 % and guarantee high accuracy SOC estimation. The maximum error of the proposed method is <2.5 %.

Distributed state-of-charge estimation for lithium-ion batteries with random sensor failure under dynamic event-triggering protocol

The state of charge (SOC) performs as an indicator of the remaining capacity of the Lithium-ion batteries (LBs). An accurate SOC estimation of LB is of great significance for its operation optimization and life extension of the battery. In this article, the issue of distributed SOC estimation is addressed for LBs. To design the distributed filter for SOC estimation, the equivalent circuit model comprised of the resistor–capacitor networks, Warburg element, ohmic resistance, battery current and voltage is established. In order to reflect the properties of the random sensor failure (RSF) well, a set of Bernoulli-distributed sequences with known probabilities is introduced. The communication resources over the wireless networks are usually limited, for the purpose of saving communication resources, the dynamic event-triggering mechanism (DETM) is adopted to regulate transmission of the signals. The main objective of this article is to design a distributed SOC estimation approach for LBs subject to RSF under DETM over the sensor networks. The upper bound of the estimation error covariance is first ensured and then such upper bound is minimized by parameterizing the estimator gain. In addition, by virtue of the matrix simplification technique, the issue of sensor network topology’s sparseness is effectively tackled. At last, experimental examples are employed to validate the feasibility of the developed distributed SOC estimation algorithm.

The state-of-charge predication of lithium-ion battery energy storage system using data-driven machine learning

Accurate estimation of state-of-charge (SOC) is critical for guaranteeing the safety and stability of lithium-ion battery energy storage system. However, this task is very challenging due to the coupling dynamics of multiple complex processes inside the lithium-ion battery and the lack of measure to monitor the variations of a battery’s internal properties. Recently, with the continuous development of Graphic Processing Unit (GPU) computing power, there is an increasing interest in applying deep-learning as SOC estimation approaches. In this paper, a novel SOC estimation scheme for lithium-ion energy storage system is proposed based on Convolutional Neural Network and Long Short-Term Memory (CNN-LSTM) neural network. This method is completely driven by the actual operating data from a photovoltaic energy storage system without using any artificial battery models or inference systems. Compared with traditional SOC estimation methods, the CNN-LSTM model can overcome the deviation in estimation caused by voltage jump at the end of charge and discharge, provide satisfied SOC estimation results during stabilized stage and various charging/discharging stages of the assembled lithium-ion batteries in the system. The calculation results indicate that this method enables fast and accurate SOC estimation with an RMSE of less than 0.31% over the entire operating data of the photovoltaic energy storage system for a full day.

Estimation of state of charge integrating spatial and temporal characteristics with transfer learning optimization

State of charge (SOC) estimation of lithium-ion batteries is of vital significance for the control strategy in battery management systems. To integrate the spatial and temporal characteristics of the data and to accomplish the transfer of knowledge, a novel convolutional neural network-bidirectional long short-term memory network based on transfer learning optimization (CNN-BiLSTM-TF) is proposed to estimate the SOC. Specifically, the spatial and temporal features hidden in the data are learned through CNN and BiLSTM, respectively. Furthermore, the CNN-BiLSTM network is established under one working condition and transferred to other working conditions through transfer learning, from which the SOC can be estimated online. A lithium-ion battery data set is applied to verify the proposed SOC estimation approach. The results of a case study demonstrate that the estimation performance of CNN-BiLSTM-TF is better than some existing approaches.

Effective estimation of the state-of-charge of latent heat thermal energy storage for heating and cooling systems using non-linear state observers

An effective quantification of the energy absorbed and supplied by latent heat thermal energy storage (LHTES) units is critical to maximise their use within thermal systems. An effective control of the charging and discharging processes of these units demands an accurate estimation of the state-of-charge (SoC). However, a direct and reliable SoC estimation requires incorporating internal sensors to monitor the temperature gradient of the phase change material (i.e. the storage medium), resulting in higher instrumentation costs and technical specifications. These issues may be relieved by adopting state observers for SoC estimation to drastically reduce the number of measurements. This paper bridges this gap by presenting a novel and direct method for estimating the SoC of LHTES units, both for heating and cooling applications, based on a non-linear state observer. The observer is based on a simple one-dimensional dynamic model of the thermal store and the thermophysical properties of the storage medium and the heat transfer fluid, which are usually provided by manufacturers. This enables the estimation of the internal temperatures of the LHTES unit and, in turn, SoC calculation. The observer implementation is simple as it requires three measurements only as input variables (i.e. the mass flow rate and the input and output temperatures of the heat transfer fluid). The SoC estimation approach is assessed through dynamic simulations of two LHTES units: one for a heating application and one for a cooling application. The results show that the SoC can be estimated with root mean square and mean absolute errors of less than 4.6% and 3.62%, respectively, compared with experimental measurements.

A State of Charge Estimation Approach for Lithium-Ion Batteries Based on the Optimized Metabolic EGM(1,1) Algorithm

The accurate estimation of the state of charge (SOC) for lithium-ion batteries’ performance prediction and durability evaluation is of paramount importance, which is significant to ensure reliability and stability for electric vehicles. The SOC estimation approaches based on big data collection and offline adjustment could result in imprecision for SOC estimation under various driving conditions at different temperatures. In the traditional GM(1,1), the initialization condition and the identifying parameter could not be changed as soon as they are confirmed. Aiming at the requirements of battery SOC estimation with non-linear characteristics of a dynamic battery system, the paper presents a method of battery state estimation based on Metabolic Even GM(1,1) to expand battery state data and introduce temperature factors in the estimation process to make SOC estimation more accurate. The latest information data used in the optimized rolling model is introduced through the data cycle updating. The experimental results show that the optimized MEGM(1,1) effectively considers the influence of initial data, and has higher accuracy than the traditional GM(1,1) model in the application of data expansion. Furthermore, it could effectively solve the problem of incomplete battery information and battery capacity fluctuation, and the dynamic performance is satisfactory to meet the requirements of fast convergence. The SOC estimation based on the presented strategy for power batteries at different temperatures could reach the goal of the overall error within 1% under CLTC conditions with well robustness and accuracy.