Review of lithium-ion battery state of charge estimation

0 Introduction

Rechargeable batteries have been widely used in batterypowered devices such as electric vehicles, unmanned aerial vehicles, fitness trackers, and Bluetooth headsets.They use different chemical compositions, such as lead acid, nickel metal hydride, and lithium ions [1].Lithium-ion batteries have become one of the most popular rechargeable batteries because of their high output voltage and energy density, long service life, and recyclability.

The battery management system (BMS) lies at the core of lithium-ion batteries.It keeps the battery pack working healthily under the working conditions recommended by the manufacturer to prolong its service life [2,3].Because of the different manufacturing processes and use environments of individual batteries, performance differences exist among the batteries, which further affects the efficiency of the whole battery pack.Therefore, the BMS monitors and controls the state of charge (SOC) of each battery pack, charges and discharges each pack reasonably, and compensates for the differences among packs.To prevent overcharge and overdischarge of batteries, the BMS requires instantaneous and accurate SOC estimation of each battery pack to provide reference for charge and discharge measurement.For this reason, real-time and accurate estimation of SOC has become a key research topic for BMSs [4,5].

Fig.1 SOC estimation steps

There are many lithium-ion batteries in each pack connected in series or parallel.The SOC of a battery pack cannot be simply equivalent to the SOC of a single battery, because there are working differences among different batteries in actual work.However, the SOC of each battery in the pack can reach the same level through balanced control.To simplify the complexity of the problem, in this study, SOC estimation of only a single lithium-ion battery is analyzed and summarized.

Generally, lithium-ion battery SOC estimation requires three steps, as shown in Fig.1.First, the lithium-ion battery model must be established.Existing lithium-ion battery models can be roughly divided into parameter-dependent models and data-dependent models.The accuracy of parameter-dependent models depends on the accurate identification of model parameters, making it necessary to introduce more accurate parameter identification methods.After determining the model and identifying the parameters, choosing a reasonable estimation method is another important research aspect of SOC estimation.In this paper, combined with the literature on lithium-ion battery SOC estimation in recent years, the advantages and disadvantages of each model and method are introduced from three aspects: the lithiumion battery model, parameter identification method, and SOC estimation method; the research topics and development directions are also summarized.

1 Lithium-ion battery model

A lithium-ion battery has a complex electrochemical mechanism and exhibits highly nonlinear behavior.Therefore, designing an easy-to-observe lithium-ion battery model is the first step in SOC estimation.Based on the research results in recent years, the commonly used lithium-ion battery models can be divided into four types: electrochemical models (EMs) [6,7], equivalent circuit models (ECMs) [8-13], fractional-order models (FOMs) [14-16], and neural network models (NNMs) [17-19].

1.1 Electrochemical models

Ems rely on a method based on electrochemical theory to describe the electronic distribution, potential change, and electrode characteristics in batteries.Partial differential equations are usually used to describe the chemical reaction process [6,7].The model is mainly used to study the battery structure design and internal reaction mechanism.The characteristics of commonly used EMs in order of accuracy from low to high are listed in Table 1.

Table 1 Comparison of the commonly used EMs

Model Advantages Disadvantages Applicability Peukert Constant current discharge is more accurate Accuracy of small current is low Constant-current discharge Shepherd Discharge voltage can be calculated Parameters are difficult to obtain Small current charge and discharge Unnewehr Accuracy is higher Error in equivalent resistor Most cases Nernst Considers polarization factor Affected by battery operating conditions Most cases

The EMs are not suitable for system-level simulation because of the complicated analysis process needed to describe the internal chemical reaction of the battery.Moreover, they have high requirements for measuring equipment and high measurement cost.In addition, using EMs requires determining numerous chemical parameters, which poses difficulties because of the large amount of calculation, sometimes including destructive tests of batteries.Consequently, EMs are often used for design purposes, which are not suitable for online application and control design of the BMS.

1.2 Equivalent circuit models

ECMs are widely used for their advantages of simple calculation and clear physical meaning.Moreover, they do not require studying the electrochemical reaction inside the battery.A circuit composed of resistors, capacitors, and constant-voltage sources is used to simulate the dynamic characteristics and capacity degradation characteristics of the battery [8-13].Typical ECMs include the Rint, RC, Thevenin, PNGV, Randle, GNL, and RCs, as shown in Fig.2.

Fig.2 Seven types of ECMs

In the Rint model, the open circuit voltage UOCV and battery internal resistance R are functions of the SOC and temperature, but the capacitive characteristics of the battery are not considered; consequently, the accuracy of this model is relatively low.In the second-order RC model, capacitor CE is introduced to describe the energy storage capacity of the battery, CC represents the polarization effect of the battery, RT is the internal resistor of the battery, and RE is the termination resistor.The second-order RC model addresses the problem of the Rint model and can better characterize the charging and discharging characteristics of the battery, but the amount of calculation is greatly increased.Compared with the second-order RC model, the Thevenin model reduces complexity by having fewer sets of RC elements, reducing the calculation amount appropriately, and is often used in engineering applications.The PNGV model is an improved model based on the Thevenin model; it characterizes battery capacity and DC response by increasing the capacitance of capacitor Cb.The Randle model is similar to the RC model, with simple parameters but low accuracy.The GNL model integrates the advantages of the above four equivalent circuit models.Not only does it well simulate the magnification response characteristics of the lithium-ion battery, but it also has wider applicability and higher simulation accuracy.The RCs model is composed of numerous time constants, and its accuracy is significantly higher than that of other models.Therefore, the dynamic response of the battery model can adapt to the voltage response of any battery terminal.Although RCs model is suitable for simulation research with complex working conditions, the calculations are more complex.

In general, the ECMs consist of several RC networks connected in series, and their voltage source corresponds to the open circuit voltage (OCV) of the battery.These models are the most commonly used and easiest to operate, but their accuracy is sometimes insufficient.

1.3 Fractional-order models

FOMs use a constant phase element (CPE) instead of the capacitor in the ECM.Compared with the ideal capacitor in the ECM, CPE in the FOM provides more accurate simulation of the double-layer behavior on the electrode, thus improving the accuracy of the model representing the battery dynamics [14-16].Corresponding to the first-order RC and second-order RC model in the Thevenin model of the ECM, the FOM is divided into the first-order RC FOM and second-order RC FOM improved by Thevenin model, as shown in Fig.3.

FOMs can better describe the nonlinear characteristics of batteries.Compared with the classical ECM, they can improve the SOC estimation accuracy and involve fewer parameters.Therefore, more and more research has been devoted to establishing FOMs for lithium-ion batteries.

Fig.3 Two types of FOMs

1.4 Neural network models

NNMs establish a nonlinear relationship between the SOC and measured variables (such as voltage, current, and temperature) by using big data learning [17-19].Fig.4 shows an NNM of the lithium-ion battery SOC estimation, in which the measured voltage, current, and temperature are taken as inputs and the SOC is taken as output to estimate the battery SOC.

Fig.4 Schematic diagram of the NNM

The NNM describes the dynamic characteristics of batteries by learning a large number of battery charging and discharging data and reduces and corrects errors through multiple training processes.The model is completely based on historical data, and its complexity is determined according to the set precision.To some extent, it effectively solves the problems of complex chemical characteristics and difficult modeling of batteries.However, the accuracy of NNM depends on the range of training data.Moreover, the accuracy of experimental data and the rationality of training methods easily affect the accuracy and generalization ability of the model.Because there are many uncertain factors in the actual operation and the training data are difficult to simulate, this type of model cannot be well adapted to practical application.

1.5 Comparison of the four models

Table 2 summarizes the advantages, disadvantages, and applicability of the four types of lithium-ion battery models.Among them, the EM has the highest accuracy.However, because there are too many parameters and destructive experiments in this model, it is often only used in battery design.The ECM has higher accuracy, but its parameters are still too numerous.Compared with the ECM, the FOM has fewer parameters and offers the same accuracy.The common disadvantage of both ECMs and FOMs is their low accuracy in variable-temperature environments.In recent years, NNMs have achieved excellent performance in SOC estimation in variable-temperature environments because of their strong nonlinear ability.However, NNMs are affected by the range of training data, and when the error between test data and training data is large, the error of SOC estimation will increase.

Table 2 Comparison of the four types of lithium-ion battery models

Model Advantages Disadvantages Applicability EM Highest accuracy Many parameters; great influence of temperature; destructive experiment Battery design ECM Higher accuracy More parameters; accuracy of variabletemperature environment is low Constanttemperature environment FOM Higher accuracy and fewer parameters Accuracy of variabletemperature environment is low Constanttemperature environment NNM Higher accuracy Depends on that range of training data Variabletemperature environment

2 Parameter identification method for the lithium-ion battery model

In Table 2, the EM is based on a chemical mechanism, which sets it apart from the other three models.Among the remaining three models, the NNM is a data-dependent model, and the ECM and FOM are parameter-dependent models that require parameter identification of key components.This section discusses the key technologies and difficulties in parameter identification for lithium-ion batteries.

2.1 Electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) is a nondestructive method for measuring parameters.When a sine wave voltage signal with frequency ω1 and a small amplitude is applied to the battery system, the system generates a sine wave current response with frequency ω2, and the change in the ratio of excitation voltage to response current is the electrochemical impedance spectrum of the system.

EIS is generally characterized by two arcs and a straight line, and each characteristic component has corresponding circuit links, which also provides a basis for the identification of the impedance spectrum.Fig.5 shows the correspondence between the electrochemical impedance spectrum and the second-order RC ECM.In the fitting process, the two arc parts and straight-line morphology can be first fit, and then the final value of the subsection local fitting can be taken as the initial value of the whole fitting, thus realizing the parameter identification of the impedance spectrum.

EIS is an offline parameter identification method.The existence of impedance spectrum measurement noise has a certain influence on the identification results of this method, particularly when the battery temperature is high and the system impedance is low.

Fig.5 Corresponding relationship between EIS and secondorder RC ECM

2.2 External characteristic fitting algorithm

The battery SOC often needs to be monitored in real time, making it necessary to dynamically identify the battery parameters online with nonlinear changes and coupling characteristics.The external characteristic fitting algorithm (ECFA) usually uses a certain equivalent model structure to simulate the external characteristics of the battery, so as to dynamically identify the model parameters.The most commonly used ECFAs include least squares (LS) and improved least squares (ILS), Kalman filter (KF), particle swarm optimization (PSO), genetic algorithm (GA), and support vector machine (SVM).Here, LS, ILS, and KF belong to the class of mathematical methods, and PSO, GA, and SVM are group intelligent algorithms (GIAs).

A.Typical mathematical method: Recursive least squares

The basic idea of the LS algorithm is to select appropriate parameters to minimize the sum of squares of the evaluation function (the difference between observed and calculated values).However, the LS algorithm needs to collect all the observed data before calculating the parameters, restricting it to offline use.Although the recursive LS (RLS) algorithm adopts the same evaluation function as the LS algorithm, each time when a group of observation data is obtained, the previous estimation value is corrected by the corresponding recurrence formula to obtain a new parameter estimation value, making the RLS algorithm suitable for online estimation [20-23].

A fixed battery model must be selected for parameter identification in the RLS algorithm.Given the tradeoff between complexity and accuracy, the Thevenin model (Fig.1(c)) is taken as an example to introduce the practical application of RLS parameter identification.The electrodynamic behavior of the Thevenin model is given by

where Up represents the polarization voltage across the parallel resistor--capacitor network; R is the internal resistor of the battery; Rp and Cp represent the polarization resistor and capacitor, respectively; IL is the load current flowing from the battery (defined as positive when discharging and negative when charging); UL is the terminal voltage, and UOCV is the OCV.

The key coefficients and model parameter identification results in the RLS algorithm are given by respectively, where Ts is the sampling time interval.

It should be noted that the RLS method is still greatly affected by noise; therefore, there are many improved methods.A bias compensation RLS method based on the Frisch scheme was proposed [24].A study suggested that the recursive form of total LS should be used to estimate the model parameters [25].In [26], a comparative study was made on the comprehensive methods of model recognition and SOC estimation, and a noise-immune model recognition using bilinear parameterization was also proposed.In [27], a recursive restricted total LS method was proposed to estimate the model parameters; this enabled addressing the situation in which only one or both of the voltage and current measurements are destroyed by noise with equal or unequal variance.Banghua D et al [28] proposed a variable forgetting factor LS method, which can better track the aging characteristics of the battery by continuously correcting and updating the forgetting factor.Song Q et al [29] designed a data loss battery working state to simulate the interference affecting the algorithm.The Thevenin model commonly used in battery management systems is used to verify the improvement in robustness of the RLS algorithm with a variable forgetting factor.

B.Group intelligent algorithm

The GIA is often used to solve nonlinear high-order equations.Because the lithium-ion battery model is nonlinear and of high order, the GIA can be applied its parameter identification.The GA is an important branch of the GIA [30], as it simulates the process of species evolution, and is a global optimal algorithm.Compared with LS parameter identification, it can identify not only the capacitor and resistor values but also the order of the capacitor [31].

In addition to the GA, other intelligent algorithms have also been applied to the solution of battery model parameters.Studies have used PSO to identify model parameters [32,33] and the simulated annealing algorithm to estimate ECM parameters, achieving good results [34].

2.3 Comparison of parameter identification methods

Table 3 summarizes the advantages, disadvantages, and applicable scope of parameter identification methods for three types of lithium-ion battery models.Among them, EIS is a method based on instrument measurement, which can accurately measure battery impedance parameters.However, this method can only be used offline and is easily affected by noise.ECFA can realize online parameter identification, but it requires data support.RLS, as a basic mathematical method, has the characteristics of a simple algorithm, but it is also easily affected by noise.Although the complex GIA can be immune to some noise effects, its implementation is relatively complex and requires considerable data support.

Table 3 Comparison of parameter identification methods

Model Advantages Disadvantages Applicability EIS Without initial parameters; high accuracy Offline method; vulnerable to noise Instrumentbased measurement RLS On-line method; simple algorithm Vulnerable to noise Data-based method GIA On-line method; higher accuracy Influenced by data; implementation is complicated Method based on large amount of data

3 SOC estimation method

Lithium-ion battery SOC estimation methods can be roughly divided into four categories, as listed in Table 4.Here, the traditional methods do not need to build a battery model and identify parameters.The ampere hour integration (AHI) method is often used to estimate the SOC of lithiumion batteries together with the OCV method.The AHI method needs to know the initial value of the SOC and the charging and discharging current information of the lithiumion batteries.If the initial value is unclear, the estimated charging state of the battery will seriously deviate from the actual value.The OCV method and internal resistor (IR) methods both establish the corresponding relationship among voltage, IR, and SOC, and then estimate the SOC according to this relationship.However, the OCV method requires a long standing time, and the IR method is greatly affected by temperature.

Table 4 Common SOC estimation methods for lithium-ion batteries

Category Specific method Traditional methods AHI, OCV, IR, etc.Observer method nonlinear observer, sliding mode observer, proportional integral observer, etc.Filter method particle filter, KF, unscented KF, extended KF, H∞ filter, etc.Intelligent algorithm neural network, fuzzy logic, SVM, genetic algorithm, etc.

Both the observer and filter methods are essentially model-based methods, and the observer method is designed by applying modern control theory to battery SOC estimation.First, by analyzing the ECM characteristics of the battery, the battery state space model expression including the SOC is established, and then the state observer is designed to estimate the value of the SOC using the control theory observer design method.This method needs strong professional knowledge of automatic control and mathematical matrix theory, making it complicated to deploy.

The filtering method is mainly based on the characteristics of correction and recursion of various filters.It has high measurement accuracy and can measure dynamic SOC.The intelligent algorithm does not depend on the model, has high recognition accuracy under the condition of sufficient data, and is suitable for computer implementation.These two methods are currently the most popular research topics in SOC estimation [6,35,36].

3.1 Filter methods in SOC estimation

The KF [37] method has advantages such as real-time performance monitoring in online recursive modeling, less demand for storage capacity during operation, and closed-loop control.KF, extended KF (EKF) [38], and unscented KF [39] are commonly used in research.The KF is an adaptive filter widely used in linear models, but it is not suitable for nonlinear models.As an extension of the KF method, the EKF method can be used in complex and nonlinear models.However, because the EKF method needs to linearize the approximation of nonlinear functions by using the first-or second-order terms of the Taylor formula and the calculation of Jacobian matrix, it is not very accurate.To overcome these shortcomings, the unscented KF has been proposed for SOC estimation; not only does it not require calculation of the Jacobian matrix, but it also has higher SOC estimation accuracy than the EKF.

However, in all the KF methods above, the statistical information of battery noise (such as model and measured noise covariance) is assumed to be accurate.If the noise statistics are not accurate, the SOC estimation based on the above KF will be unstable or even divergent, and the adaptation speed becomes too slow [40].To solve these problems, the adaptive KF, adaptive EKF [41], and adaptive unscented KF [42-44] are used to estimate noise statistics online, but they entail extra calculation cost.

Only when the statistical characteristics of system noise are predicted can the KF filtering algorithm get better estimation results.Therefore, the real accuracy of KF filtering in SOC estimation often cannot meet the engineering requirements.If the accurate prior information of the system cannot be predicted, it is necessary to increase the value of the noise covariance matrix when designing the KF to increase the utilization weight of real-time measurement and reduce the utilization weight of one-step prediction.This method is commonly known as tuning.However, there is blindness in tuning, and it is impossible to determine how much the value of the noise covariance matrix will increase to achieve the best estimation accuracy.Moreover, if the measurement noise and process noise of the system are not white noise, or if there is deviation, the effect of Kalman filtering will be severely deteriorated or even divergent.

In the KF estimation model, both noise and measurement noise are assumed to be Gaussian white noise with a mean value of zero.In practical applications, it is difficult to realize this assumption, because the noise from environmental interference may explain the biased distribution, which will negatively affect the accuracy and convergence behavior of SOC estimation using s KF.To solve this problem, particle filter and unscented particle filter methods [45,46] are studied to estimate battery SOC.However, because of the large number of computational requirements and high memory consumption, these filters are not suitable for online SOC estimation in practical applications.The H∞ filtering algorithm is also used to estimate the SOC of batteries.The H∞ filtering algorithm only requires the noise signal of the system to be a random signal with limited energy and does not require a prediction of accurate noise statistical characteristics and can obtain the minimum estimation error under the condition of high noise interference [47,48].The design idea of the H∞ filtering algorithm is to minimize the influence of system process noise, measurement noise, and uncertainty of initial state variables on estimation accuracy under the condition of unknown estimation noise, measurement noise, and error, thereby minimizing the estimation error of the filter under the worst conditions.Therefore, the H∞ filtering algorithm can be regarded as the optimal filtering when the system has serious interference [49,50].

3.2 Intelligent algorithms in SOC estimation

Although great progress has been made in modern sensor technology, it is still impossible to actually measure SOC outside the laboratory in a controlled environment.However, because the SOC has a good correlation with some observable quantities (such as battery voltage, current, and temperature), these quantities are usually used to estimate SOC.Intelligent algorithms are the most widely used high-order algorithms for estimating SOC based on observation.

The commonly used intelligent algorithms in SOC estimation are SVM and artificial neural networks [7,38,51].However, these methods have two defects that affect the performance of SOC estimation.First, the input data are the feature information extracted from the original data, which need manual design and require considerable manpower and professional knowledge.Second, the model structure adopts a shallow learning architecture, which has insufficient analytical ability and makes handling high-dimensional data difficult.

As an important branch of machine learning, deep learning provides an effective solution to the above problems.Using deep learning technology, one can construct a deep neural network (DNN) by using a multilayer nonlinear transformation and extract complex feature information from input data hierarchically.Therefore, the end-to-end estimator can be implemented based on a DNN to automatically learn the internal representation from the original signal and realize the SOC estimation of the lithium-ion battery.Recently, several SOC estimation methods based on DNNs have been proposed.In [52], an SOC estimator was constructed by using a multilayer perceptron network, and the estimator was trained by using signals measured at different ambient temperatures.The results demonstrated that the trained model can reduce the estimation error of the SOC.On the basis of this research, the advantages of using a long short-term memory (LSTM) network in capturing time information from time series data have been considered.Tian Y et al and Yang F et al [53, 54] developed an estimator based on the LSTM network to further improve the estimation accuracy and achieved good results.As another variant of the recurrent neural network (RNN), gated cyclic unit (GRU) networks have also been applied to SOC estimation.In [18,55], a GRU structure was introduced into an RNN to improve the modeling ability of the nonlinear behavior of lithium-ion batteries, and two models using current and voltage signals as inputs were constructed to estimate the SOC.A simple estimation model based on the GRU was proposed, which was applied to two lithium-ion battery data sets to effectively estimate the SOC at different ambient temperatures [56,57].

Compared with the traditional SOC estimation method, the above method based on RNN has the following three advantages: 1.The RNN can directly map the battery measurement data to the SOC value without other battery models depending on the operating parameters.2.The RNN can learn the weight and deviation by using the gradient descent algorithm, which is quite different from the mathematical model requires significant effort to design and parameterize manually.3.The RNN with a set of network parameters can realize SOC estimation under various ambient temperatures, while other traditional methods need models with different parameters for different working conditions.

3.3 Comparison of the SOC estimation methods

Table 5 compares the principles, advantages, and disadvantages of SOC estimation methods commonly used at present.In general, traditional methods have clear physical meaning and are relatively simple to implement, but they often need additional equipment and are generally offline methods, which are greatly affected by the environment.At present, the development direction of traditional methods is toward anti-interference online methods.Model-based methods can realize online recognition, but they often need to build complex models, and the implementation process is cumbersome.Their accuracy is affected by both model accuracy and environmental noise, and their development direction is toward new anti-interference high-precision methods.Intelligent algorithms do not depend on models, give full play to the learning ability of computers, and simulate the process of human judgment and recognition.However, their results depend on the accuracy, rationality, and sufficiency of data collection, and their implementation is more complex.Their development direction is toward new intelligent methods with low complexity and high accuracy and less dependence on data.

Table 5 Principle, advantages, and disadvantages of SOC estimation methods

Method Principle Advantages Disadvantages AHI Integrates the current under the known initial SOC value Less affected by battery; high online measurement accuracy Extremely high requirements for SOC initial value; measurement errors are accumulated OCV Nonlinear relationship between OCV and SOC Accurate calculation when the battery is stationary Not suitable for online SOC estimation IR Relationship between internal resistor and SOC High accuracy in the later period of discharge Complex; greatly affected by temperature; rarely used in realtime monitoring Observer method Principle of control theory observer High precision; accurate dynamic SOC Complex implementation,vulnerable to noise and vibration Filter method Recursion of state equation and measurement equation High precision; accurate dynamic SOC High accuracy; complex operation Intelligent algorithm Learning ability of intelligent algorithm to simulate nonlinear battery characteristics High precision; accurate dynamic SOC Requires many data; greatly influenced by training data

Table 5 is a comparison of single methods.In fact, research in recent years has demonstrated that the accuracy of single methods cannot be greatly improved.Even if more advanced equipment and technology are adopted, the SOC with hybrid methods has gradually shown advantages, such as use of data-driven and model-driven hybrid algorithms.A hybrid SOC and output voltage prediction method that combines a vector autoregressive moving average and an LSTM algorithm to improve prediction accuracy have been proposed [58].Additionally, a study proposed a hybrid method of retaining useful life prediction and state of health diagnosis in which support vector regression is used to establish the battery capacity degradation model and a particle filter is used to estimate the degradation parameters according to the impedance measurement value of each cycle [59].In [60], an improved particle filter and AHI algorithm was proposed to improve the accuracy of SOC estimation.In [61], A fusion algorithm based on the RLS method with a forgetting factor, EKF, and correlation vector machine algorithm was proposed.This algorithm can effectively eliminate the estimation error in the SOC caused by uncertainty of statistical characteristics of model error and measurement noise and has good convergence and robustness.

4 Conclusion

Performance optimization of lithium-ion batteries is the focus of research on EVs.Given its importance and complexity, improving the accuracy of SOC estimation of lithium-ion batteries has become an important task in BMS optimization and an important research direction in the future.Based on the existing technologies, subsequent research will focus on the following points:

(1) ECMs and FOMs are the mainstream lithium-ion battery models.We should study the polarization effect of the IR, charging and discharging efficiency, and other factors that affect the temperature and create a general model suitable for all types of batteries.However, reducing the amount of parameter calculations on the premise of realtime accuracy is also a problem to be solved in the future.

(2) In parameter identification in ECMs and FOMs, the latest intelligent algorithms such as the ant colony, grey wolf, bat, and whale algorithms can be introduced to improve the accuracy and speed of parameter identification.

(3) The SOC estimation algorithm based on the KF faces the problem of how to improve the estimation efficiency and real-time performance while ensuring the convergence of the optimization process.Particle and H∞ filters can indeed eliminate this situation.Therefore, the selection and optimization of many nonlinear filter algorithms still becomes the center of SOC estimation algorithms.

(4) SOC estimation methods based on intelligent algorithms depend on the quality and quantity of training data, and the training process may take considerable time.However, with the accumulation of data and continues computer development, these problems can be solved easily.

(5) The difference in battery polarity materials will also lead to some differences in their characteristics.We can try to study different types of batteries made of different materials.At the same time, the influence of constantly updated new polarity materials on battery SOC estimation will also become a key development topic.

(6) Modularization will be the main direction of development in all fields of the manufacturing industry in the future.Similarly, SOC analysis and estimation for modular battery packs will certainly become an important direction of development.

Acknowledgements

This work was supported by research on value model and technology application of patent operation of science and technology project (52094020000U); National Natural Science Foundation of China (52177193).

Declaration of Competing Interest

We have no conflict of interest to declare.