In the context of global energy transition and carbon reduction strategies, the new energy industry has experienced rapid development. Due to key characteristics such as high energy density and long cycle life, the li ion battery has become a crucial energy storage technology in the current clean energy sector. To ensure that battery systems maintain stable performance and longevity under complex operating conditions, the Battery Management System (BMS) plays a pivotal role, and the estimation of State of Charge (SOC) is a foundational task of the BMS. Accurate SOC estimation is a fundamental prerequisite for optimizing the usage efficiency of the li ion battery and ensuring system safety and reliability. The development of high-precision SOC estimation technology remains a focal point in BMS research. In this article, I will comprehensively review the research progress in SOC estimation methods for li ion batteries, analyzing from four aspects: direct measurement methods, model-based methods, data-driven methods, and model-data fusion-driven methods. I will compare the technical advantages, applicable scenarios, and limitations of different estimation methods, summarize existing challenges, and outlook future development trends.
The li ion battery is a complex electrochemical system with nonlinear and time-varying characteristics, making SOC estimation a challenging task. SOC is defined as the ratio of the remaining capacity to the maximum available capacity of the battery, typically expressed as a percentage. Accurate SOC estimation not only enhances the operational efficiency of electric vehicles and energy storage systems but also prevents overcharge and over-discharge, thereby extending the lifespan of the li ion battery. Over the years, numerous methods have been proposed, each with its own strengths and weaknesses. I will delve into these methods, providing detailed explanations, formulas, and comparative tables to offer a comprehensive understanding.
Direct Measurement Methods
Traditional SOC estimation strategies for li ion batteries are based on experimentally measured battery parameters. These methods are straightforward but often come with limitations in dynamic applications. The primary direct measurement methods include the Open Circuit Voltage (OCV) method and the Ampere-Hour (AH) integration method.
Open Circuit Voltage (OCV) Method
The OCV method estimates SOC by measuring the voltage of the li ion battery when no current is flowing. The core of this method lies in the nonlinear relationship between the battery’s OCV and SOC, typically showing that OCV gradually increases as SOC rises. In an ideal state, by measuring OCV and referring to a lookup table, SOC can be obtained. The mathematical representation is:
$$x_{SOC} = f^{-1}(x_{OCV})$$
where \(x\) is the state variable and \(f^{-1}\) is the inverse function. The OCV method requires high-precision sensing equipment to obtain accurate voltage readings, and before measurement, sufficient time must be allowed for the battery voltage to stabilize. These limitations make this method unsuitable for dynamic applications. To overcome the drawback of traditional OCV requiring long rest periods, the Predicted Static OCV (PSOCV) method has been proposed. This method is based on a second-order RC equivalent circuit model, combined with Euler forward difference for state equation discretization, and uses linear interpolation (LI) technology to optimize parameter fitting, suppressing voltage fluctuations caused by polarization effects. Under Hybrid Pulse Power Characterization (HPPC) and Urban Dynamometer Driving Schedule (UDDS) conditions, the average absolute error of SOC estimation can be stabilized within 1%, improving estimation efficiency and feasibility for embedded applications.
Ampere-Hour (AH) Integration Method
The AH integration method estimates SOC based on the current and voltage relationship during the charge and discharge processes of the li ion battery. The core is to measure the charge and discharge current and voltage, combined with battery capacity parameters, to calculate SOC. The formula is:
$$(x_{SOC})_t = (x_{SOC})_0 – \frac{1}{Q_n} \int_0^t \eta I(\tau) d\tau$$
where \(\eta\) is the Coulombic efficiency, \(I\) is the instantaneous current, \(\tau\) is the time moment, \(t\) is the time variable, and \(Q_n\) is the rated capacity. The AH integration method has low computational complexity, but since battery capacity dynamically changes with battery aging, integration errors accumulate over time with increasing cycle counts. To address this, a multi-variable Long Short-Term Memory (LSTM) network has been constructed, selecting four key influencing factors—voltage, current, temperature, and cycle count—as LSTM inputs, capturing nonlinear temporal features of capacity decay through a forget gate mechanism. Compared to the traditional AH integration method, this approach reduces SOC estimation error over the full lifecycle of the li ion battery by more than 50%, making it particularly suitable for electric vehicle BMS systems.
Comparison of Traditional SOC Estimation Techniques
Other traditional SOC estimation techniques for li ion batteries include conductance method, discharge test method, and AC impedance method. The advantages and disadvantages of these methods are summarized in the table below.
| Estimation Technique | Advantages | Limitations | Applicable Scenarios |
|---|---|---|---|
| OCV Method | Simple and intuitive principle, high accuracy in static state | Requires long rest periods, flat voltage change in mid-SOC range, error increases significantly at low temperatures | SOC initialization for stationary vehicles, laboratory offline calibration, energy storage systems with low real-time requirements |
| AH Integration Method | Real-time online monitoring, fast dynamic response, low hardware cost | Current error accumulation amplifies, depends on initial SOC accuracy, requires compensation for Coulombic efficiency changes | On-board continuous monitoring systems, dynamic condition tracking |
| Conductance Method | Simple principle, fast detection speed, high sensitivity in low SOC region | Requires precise measurement instruments, highly influenced by temperature | Battery discharge termination judgment, electrolyte performance research |
| Discharge Test Method | Relatively true and reliable results, no mathematical model needed | Destructive testing accelerates aging, time-consuming | New battery capacity calibration, offline benchmark testing |
| AC Impedance Method | High accuracy, can identify internal state changes | Requires high-frequency excitation equipment, interfered by multiple factors such as temperature and aging, fails in dynamic conditions | Laboratory precise calibration, State of Health (SOH) research |
From the table, it is evident that the conductance method and AC impedance method require high precision in measured parameters and need precise measurement instruments; the discharge test method and OCV method have high accuracy but are time-consuming; the AH integration method can achieve online monitoring, while the other four methods cannot obtain SOC in real time. The li ion battery’s performance is highly dependent on these estimation techniques, and selecting the appropriate method is crucial for specific applications.
Model-Based Methods
The effectiveness of model-based SOC estimation methods highly depends on the accuracy and complexity of the selected battery model. Currently, models used to describe the external characteristics of li ion batteries are mainly divided into two categories: Equivalent Circuit Models (ECM) and Electrochemical Models (EM).
Estimation Methods Based on Equivalent Circuit Model (ECM)
Battery SOC estimation based on ECM is typically achieved by combining estimation methods based on filters. Optimization algorithms based on the Kalman Filter (KF) principle are currently the mainstream direction in research and application. The classic KF is designed for linear, time-invariant systems, whereas the internal electrochemical processes of li ion batteries exhibit significant nonlinear and time-varying characteristics, making the classic KF algorithm difficult to provide reliable estimates. The traditional Iterated Extended Kalman Filter (IEKF) tends to ignore higher-order terms in strongly nonlinear systems, leading to issues such as slow convergence speed and error accumulation. To address this, an improved Iterated Extended Kalman Filter (LM-IEKF) has been proposed, embedding Levenberg-Marquardt (LM) optimization into the IEKF iterative framework, dynamically adjusting the covariance matrix through a damping factor. Using HPPC parameter identification datasets and Federal Urban Driving Schedule (FUDS) and Beijing Dynamic Stress Test (BJDST) conditions for validation, it was found that the maximum error of LM-IEKF is less than 1.98% (compared to 2.74% for traditional IEKF), and the average error can be reduced to 0.47%–0.58%. Some research on SOC estimation methods based on ECM is summarized in the table below.
| Algorithm Name | Algorithm Improvement Description | Improvement Effect |
|---|---|---|
| Recursive Gradient Correction (RGC)-Multi-Innovation Unscented Kalman Filter (MIUKF) Algorithm | Parameter identification along the negative gradient of the criterion function, introducing an innovation matrix, fusing historical errors | Parameter identification speed under UDDS conditions is 0.13 s (compared to 0.19 s for Forgetting Factor Recursive Least Squares), maximum error reduced to 2.0% (Unscented Kalman Filter (UKF) maximum error is 3.5%) |
| ECM (EQ)-OCV-Ah-Extended Kalman Filter (EKF) Scheme | Parameter identification uses Genetic Algorithm (GA) + LM instead of a single algorithm, uses EKF linearization of state equations to estimate SOC | Mean Absolute Error (MAE) is 0.0027 (compared to 0.0067 for EQ-OCV-Ah scheme and 0.0035 for EQ-Support Vector Machine (SVM) scheme) |
| Multi-Innovation Adaptive Robust UKF | Multi-innovation theory fuses historical data, H∞ filtering suppresses colored noise, multi-time scale | Under full temperature range of 10–40°C, maximum SOC error is 1.05%, Root Mean Square Error (RMSE) is 0.42% |
The li ion battery’s behavior in dynamic conditions necessitates robust algorithms like these to ensure accurate SOC estimation. The ECM-based approaches are favored in engineering practice due to their simplicity and computational efficiency, but they may lack the ability to track internal electrochemical states, which is crucial for advanced BMS in modern electric vehicles.
Estimation Methods Based on Electrochemical Model (EM)
In practical engineering applications, ECM, with its simple structure and high computational efficiency, has become the mainstream choice in current engineering practice. However, its ability to track the internal electrochemical state of the li ion battery is limited, making it insufficient to meet the needs of advanced BMS for vehicle power batteries. In contrast, EM can better combine electrochemical mechanisms with changes in internal battery parameters to estimate SOC, gradually becoming a research focus for SOC estimation of li ion batteries.
Traditional observers ignore the relationship between fractional-order element differences and SOC, leading to inaccurate estimation. A non-commensurate fractional-order observer combined with an improved Adaptive Fractional-Order Particle Swarm Optimization (AFOPSO) algorithm has been proposed. By designing a non-commensurate fractional-order observer to capture the fractional-order characteristics of the battery, under FUDS conditions, the maximum error is 2.58%, and the time consumption is less than that of EKF and FEKF algorithms. Traditional Sliding Mode Observer (SMO) suffers from output chattering issues and is sensitive to model parameter changes. An Adaptive Sliding Mode Observer (ASMO) combined with a simplified hysteresis model has been proposed, introducing an adaptive gain adjustment mechanism to suppress chattering phenomena in traditional SMO. Under FUDS conditions, MAE is 0.70%, maximum error is 4.00%, and it converges faster than traditional SMO and EKF. Some research on SOC estimation methods based on EM is summarized in the table below.
| Algorithm Name | Algorithm Improvement Description | Improvement Effect |
|---|---|---|
| Simplified EM Model + Proportional-Integral Observer | Volume average method simplifies Pseudo-Two-Dimensional (P2D) model, uses proportional-integral observer to reduce computational complexity | Under Dynamic Stress Test (DST) conditions, maximum absolute error of SOC estimation is only 0.18%, computation time shortened |
| Adaptive Gain Nonlinear Observer (AGNO) | Gain nonlinear adaptive adjustment, solves poor adaptability under variable conditions | Switching error during rate change < 0.5%, error in full temperature range of 20–60°C < 1.8% |
| Multi-Objective Optimization Observer | Pareto optimization of observer gain and observation function, improves contradiction between convergence speed and accuracy | Under FUDS conditions, RMSE is 0.58%, convergence speed < 5 s (3 times faster than EKF) |
The electrochemical model provides a more detailed insight into the li ion battery’s internal processes, which is essential for high-fidelity SOC estimation. However, the computational burden is higher, and real-time implementation can be challenging. Therefore, simplifications and optimizations are necessary to make EM-based methods practical for BMS applications.
Data-Driven Methods
Model-based SOC estimation methods have clear theoretical foundations and relatively standardized design processes, but estimation accuracy is limited by the accuracy of the constructed models. The complex internal electrochemical reaction processes of li ion batteries are difficult to fully and accurately represent with mathematical models, and battery parameters exhibit significant time-varying characteristics during use, bringing inevitable errors to the models. Data-driven SOC estimation methods have received widespread attention from researchers in recent years. Currently, machine learning algorithms applied to SOC estimation of li ion batteries mainly include Artificial Neural Networks (ANN), Support Vector Machines (SVM), and other methods.
Neural Network-Based Estimation Methods
Traditional ANN has been used to estimate SOC for li ion batteries, comparing the performance of Feedforward Neural Networks (FNN) and Recurrent Neural Networks with Long Short-Term Memory units (RNN-LSTM) in SOC estimation. Based on experiments under the Worldwide Harmonized Light Vehicles Test Procedure (WLTP) driving conditions, FNN trains faster (taking less than 1 minute) with an average RMSE of 2.06%, making it suitable for scenarios with limited computational resources or requiring rapid deployment. However, it may have limitations when handling complex data. RNN-LSTM training takes about 6 minutes with an average RMSE of 2.37%. RNN-LSTM introduces gating mechanisms, reduces dynamic response lag, and better handles temporal characteristics of data, making it suitable for scenarios with higher requirements for SOC estimation accuracy. Some research on neural network-based SOC estimation methods for li ion batteries is summarized in the table below.
| Algorithm Name | Algorithm Improvement Description | Improvement Effect |
|---|---|---|
| LSTM + Adam Optimization + Dropout Regularization | Adam optimizer dynamically adjusts learning rate, accelerates convergence, Dropout reduces overfitting, enhances robustness | MAE reduced to 0.11%–1.68%, in cross-aging battery generalization tests, MAE below 2% |
| Grey Wolf Optimizer (GWO)-Gated Recurrent Unit (GRU) Model | GWO optimizer globally searches GRU hyperparameters, GRU gating units enhance long-sequence memory capability | RMSE < 0.9%, model stability improved, error standard deviation reduced |
| Simple Recurrent Unit (SRU) Joint Estimation Framework (SOC/SOH) | SRU directly outputs SOC, based on charge integration infers SOH | SOC estimation RMSE < 0.95%, SOH estimation RMSE < 0.93%, cross-battery type generalization error < 2.3% |
The li ion battery’s SOC estimation benefits greatly from neural networks due to their ability to learn complex nonlinear relationships from data. However, these methods require large amounts of high-quality training data and may suffer from overfitting if not properly regularized. The choice between FNN and RNN-LSTM depends on the specific application requirements, such as real-time constraints and available computational resources.
Support Vector Machine-Based Estimation Methods
SVM, with its nonlinear modeling capabilities and advantages in small sample scenarios, has become an important tool for SOC estimation of li ion batteries. Recent research has mainly focused on two aspects: parameter optimization and model structure improvement, by introducing various intelligent optimization algorithms for efficient parameter tuning. Compared to neural network-based algorithms, SVM achieves nonlinear mapping through kernel functions, and SVM performs well under small sample conditions, making it particularly suitable for scenarios with limited experimental data in battery SOC estimation.
Addressing the issue of fixed kernel function parameters in traditional SVM leading to insufficient adaptability, a method based on Particle Swarm Optimization (PSO) for SVM has been proposed. The penalty parameter and kernel width are encoded as particle positions, and through velocity update formulas, globally search for the solution with minimum RMSE. Key points of SOC time and voltage features are extracted to construct an SOH estimation function, avoiding high-dimensional inputs. Simultaneously, SOC estimation results are fed back to the SOH model in real-time, forming a closed-loop optimization. Under laboratory DST conditions, the RMSE of SOH estimation for PSO-SVM is reduced to 2.45% (compared to 4.18% for traditional SVM). Some research on SVM-based SOC estimation methods for li ion batteries is summarized in the table below.
| Algorithm Name | Algorithm Improvement Description | Improvement Effect |
|---|---|---|
| Improved Fruit Fly Algorithm (IFOA)-Least Squares Support Vector Machine (LSSVM) | Introduces adaptive relaxation term, expands search range, avoids local optima | SOC estimation MAE reduced to 1.02% |
| Multi-Mode Ensemble Support Vector Regression (ME-SVR) | Uses clustering algorithm to establish independent SVR models for each subset, then integrates results through weighted averaging | Solves issues of low accuracy and poor generalization performance of single models under mixed conditions |
| Adaptive PSO Optimized LSSVM | Improves PSO inertia weight, balances global and local search capabilities | RMSE reduced to 1.63% (compared to 2.65% for PSO-LSSVM and 4.57% for SVM) |
The li ion battery’s SOC estimation using SVM-based methods offers a good balance between accuracy and computational efficiency, especially when data is scarce. The integration of optimization algorithms like PSO enhances the performance by automating the parameter selection process, which is often tedious and suboptimal when done manually.
Model-Data Fusion-Driven Methods
Due to the strong time-varying nature of battery parameters, model-based methods struggle to identify parameter changes in real-time, while data-driven estimation methods rely on large amounts of high-quality data for model training. Researchers have combined these two approaches to estimate battery SOC. Currently, fusion methods are mainly divided into two types: data-driven fusion and model-data driven fusion.
Traditional UKF with fixed parameters can easily lead to parameter drift issues, resulting in poor model accuracy. A SOC estimation method based on Forgetting Factor Recursive Least Squares (FFRLS) and Adaptive Unscented Kalman Filter (AUKF) has been proposed. With a forgetting factor λ = 0.98, it updates equivalent circuit parameters online, suppressing interference from historical data. Simultaneously, based on aging experimental data, a capacity degradation model is constructed to correct the maximum available capacity in real-time. In experiments with a dataset of 2,160,000 points under UDDS conditions, SOC estimation error remains stable below 1.5%, converging within 5 minutes under an initial 10% deviation, with improved accuracy compared to traditional UKF. A fusion method based on ECM and Backpropagation Neural Network has been proposed. Using a second-order RC equivalent circuit, through HPPC testing, a three-dimensional mapping of OCV-SOC-temperature is established to estimate the initial SOC with temperature compensation. Then, with EKF output, voltage, current, and temperature as inputs, through tansig activation function, time-varying nonlinear errors are learned. Experimental results show that under full temperature range of -20 to 20°C and rates of 0.3 to 2.0 C, the RMSE of the fusion model remains stable below 0.49%. Other research on model-data fusion-driven SOC estimation methods for li ion batteries is summarized in the table below.
| Algorithm Name | Algorithm Improvement Description | Improvement Effect |
|---|---|---|
| Neural Network + EKF | Neural network provides high-precision estimation, EKF performs dynamic correction, solves feature ambiguity issues in aged low-capacity batteries | After 300 cycles, RMSE < 1.5% |
| Reinforcement Learning (RL) + KF | RL optimizes model parameters and filter weights, solves filter inaccuracy issues under variable conditions | Under variable conditions (-10°C to 45°C), MAE reduced to 0.89% |
| Federated Learning (FL) Fusion Framework | Distributed training under FL framework, improves model generalization capability and privacy protection | In cross-vehicle testing, RMSE reduced from 1.92% to 1.19% |
The li ion battery’s SOC estimation through model-data fusion represents a promising direction, as it leverages the strengths of both approaches: the interpretability and physical basis of models, and the adaptability and pattern recognition capabilities of data-driven methods. However, fusion methods may also introduce the limitations of both, such as increased complexity and the need for careful integration to avoid conflicts. Future research should focus on optimizing these fusion strategies to achieve robust and accurate SOC estimation across diverse operating conditions for the li ion battery.
Conclusion and Outlook
In this article, I have primarily introduced the SOC estimation methods for li ion batteries and reviewed the current research status of these methods. Currently, mainstream SOC estimation methods for li ion batteries can be classified into direct measurement methods, model-based methods, data-driven methods, and model-data fusion-driven methods. The li ion battery is a very complex nonlinear time-varying system; therefore, the main challenge for model-based methods is the difficulty in establishing a model that better reflects the real parameter changes of the battery. Data-driven methods face issues such as insufficient computational power on vehicle platforms and poor generalization capability. Model-data fusion-driven methods, while combining the advantages of different estimation methods, may also introduce the limitations of each method. Overall, many new estimation methods with excellent performance are still in the experimental stage and have not been widely promoted in engineering applications. Future research on SOC estimation for li ion batteries should focus on how to better integrate different estimation methods and achieve promotion in engineering applications.
Several key trends are emerging in the field of SOC estimation for li ion batteries. First, there is a growing emphasis on adaptive algorithms that can adjust to battery aging and varying environmental conditions. The li ion battery’s performance degrades over time, and SOC estimation methods must account for this degradation to maintain accuracy throughout the battery’s lifecycle. Second, the integration of artificial intelligence and machine learning with traditional model-based approaches is becoming more sophisticated, enabling real-time learning and correction. Third, there is increasing interest in multi-state estimation, where SOC is estimated alongside other states like State of Health (SOH) and State of Power (SOP), providing a comprehensive view of the li ion battery’s condition.
Moreover, the development of low-cost, high-precision sensors and edge computing capabilities will facilitate the implementation of advanced SOC estimation algorithms in practical BMS. Standardization of testing protocols and data sharing across industries can also accelerate progress by providing diverse datasets for training and validation. Ultimately, the goal is to achieve reliable, accurate, and real-time SOC estimation for li ion batteries in all applications, from electric vehicles to grid storage, ensuring safety, efficiency, and longevity.
In conclusion, the journey towards perfecting SOC estimation for li ion batteries is ongoing, with each method contributing valuable insights. By leveraging the synergies between different approaches and addressing their individual limitations, we can move closer to optimal battery management and a sustainable energy future.