With the rapid advancement and integration of renewable energy sources, electrochemical energy storage systems have become pivotal in balancing energy supply and demand, enhancing energy utilization efficiency, and ensuring grid stability. Among various energy storage devices, the lithium iron phosphate (LiFePO4) battery stands out due to its high energy density, long cycle life, environmental friendliness, and superior safety profile. These attributes make LiFePO4 batteries highly suitable for large-scale electrochemical energy storage applications, where reliable performance and management are critical. A key aspect of battery management is the accurate estimation of the State of Charge (SOC), which represents the remaining capacity of the battery as a percentage of its total capacity. Accurate SOC estimation is essential for preventing overcharge and over-discharge, optimizing battery usage, prolonging battery lifespan, and improving overall system efficiency. However, traditional SOC estimation methods for LiFePO4 batteries often rely on periodic or timed estimation approaches, which suffer from limited coverage and can lead to significant errors in the final estimates. Furthermore, many existing estimation methods employ unidirectional structures that are inefficient and lack robustness, contributing to inaccuracies in SOC determination. These limitations are exacerbated by the nonlinear dynamic characteristics of batteries, inconsistent charging and discharging conditions, and complex aging processes, all of which pose challenges for precise SOC tracking. To address these issues, this research proposes a comprehensive approach for SOC estimation of LiFePO4 batteries in electrochemical energy storage systems. By designing a more flexible and stable estimation framework, we aim to enhance estimation performance from multiple angles, rigorously control each processing step, and mitigate the impact of battery nonlinearities and aging. This study breaks the constraints of initial SOC estimation, providing a solid foundation for subsequent applications and调度, thereby advancing the management of LiFePO4 battery systems.
The core of our methodology involves calculating SOC estimation compensation coefficients, establishing multi-order observation equations, designing a deep neural network-based SOC estimation model, and implementing OCV verification correction. Each step is meticulously crafted to overcome the shortcomings of conventional methods. Firstly, we compute the SOC estimation compensation coefficient to account for variations in battery behavior under different operating conditions. This coefficient is derived from the actual recursive relationship of the battery SOC, which is expressed as:
$$ \text{SOC}(k) = \text{SOC}(k-1) + \frac{\Delta \iota_1(k-1) \chi}{\iota_2} $$
where \(\text{SOC}(k)\) denotes the SOC at step \(k\), \(\iota_1\) and \(\iota_2\) represent the initial and actual charge values, respectively, and \(\chi\) is the battery operating frequency. Based on this recursive relationship, we define an exponential function within the ratio of capacity at different discharge rates to capacity at 1C discharge rate, enabling recursive fitting to calculate the compensation coefficient \(B\):
$$ B = o^2 – \sum_{z=1}^{n} \vartheta_z + \gamma $$
Here, \(o\) is the battery health coefficient, \(\vartheta_z\) is the mean capacity at temperature \(z\), \(n\) is the number of temperature points, and \(\gamma\) represents the cycle discharge count. This compensation coefficient serves as a predictive guide, adapting to rate changes and facilitating accurate SOC estimation. Subsequently, we establish a multi-order observation equation to capture the battery’s dynamics across multiple cycles. This equation is formulated as:
$$ \begin{bmatrix} D_j(g) \\ D_w(g) \\ \text{SOC}(k) \end{bmatrix} = \begin{bmatrix} e^{\Delta f – \partial} & 0 & 0 \\ 0 & e^{+\frac{1}{\Delta f – \partial}} & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} D_j(g-1) \\ D_w(g-1) \\ \text{SOC}(k-1) \end{bmatrix} $$
In this equation, \(D_j(g)\) and \(D_w(g)\) denote polarization voltages at step \(g\), \(\Delta f\) is the temperature change, \(\partial\) is the input vector, and \(e\) is the output vector. This multi-order approach expands the estimation range beyond traditional point measurements, allowing for comprehensive observation of battery behavior and SOC variations over time. The observation equation integrates key parameters such as voltage, current, and temperature, enabling real-time data acquisition and analysis. To further enhance estimation accuracy, we leverage deep neural network (DNN) technology to design a SOC estimation model specifically for LiFePO4 batteries. The model processes inputs like voltage, current, and temperature fluctuations to estimate SOC. Under different frequencies, small-amplitude sinusoidal current signals induce AC impedance in the battery. By correlating this impedance with SOC states using the established observation equation, we analyze the impedance characteristics of the LiFePO4 battery. The DNN model is trained on extensive datasets to learn complex nonlinear relationships between battery parameters and SOC. The workflow of the DNN-based SOC estimation model involves data collection, feature extraction, network training, and SOC prediction. The model’s SOC estimation result \(\xi\) is given by:
$$ \xi = (1 – \zeta^2) \times \upsilon $$
where \(\zeta\) is the impedance change feature value, and \(\upsilon\) is the current difference. This model provides preliminary SOC estimates, which are then refined through OCV verification correction. OCV correction is a crucial step that leverages the known relationship between open-circuit voltage and SOC to adjust the model outputs. We measure the battery’s OCV under resting conditions and apply temperature and aging compensations to account for external factors that may affect the OCV-SOC mapping. The OCV verification process involves comparing the measured OCV with pre-established OCV-SOC curves, deriving correction factors, and updating the SOC estimates accordingly. This iterative correction ensures high precision and reliability in the final SOC values, even under varying operational scenarios.
To validate the effectiveness of our proposed SOC estimation method for LiFePO4 batteries, we conducted extensive testing under controlled laboratory conditions. The testing environment was set up using MATLAB software for simulation and data analysis, ensuring reproducibility and accuracy. We configured the test parameters to reflect real-world electrochemical energy storage system operations. The LiFePO4 battery used in tests had a rated capacity of 25 Ah, with upper and lower cutoff voltages set at 4.25 V and 2.16 V, respectively. The sampling frequency was fixed at 1.25 Hz, and the ambient temperature was maintained at 25°C to minimize external influences. The battery control system was equipped with sensing devices to collect real-time data on voltage, current, and temperature. Key auxiliary test indicators were defined to guide the evaluation process, as summarized in the table below:
| Auxiliary Test Indicator Item | Parameter Standard Value |
|---|---|
| Open-Circuit Voltage (V) | 6.5 |
| Constant Current Discharge (A) | 10–12 |
| Static Capacity (Ah) | 20–28 |
| Ambient Temperature Variation Range (°C) | 18–25 |
These parameters ensured a consistent baseline for comparing SOC estimation performance across different test cycles. We performed a standard 50C pulse discharge test on the LiFePO4 battery, with discharge intervals ranging from 0.3 to 0.5 seconds. Each pulse discharge cycle was set to 0.1 seconds, during which we collected high-resolution voltage and current data. The data acquisition process involved amplifying specific segments to capture detailed transient responses, as illustrated in the voltage and current plots. When the battery was fully charged, the state of health coefficient was set to 1, and the initial SOC was standardized at 100%. Using the acquired current and voltage data, we assessed the battery’s operational status and performed SOC estimation. The terminal voltage \(F\) under different resistance conditions was calculated to verify estimation accuracy:
$$ F = \sum_{U=1}^{m} A_U – \frac{m_2^2}{m_1 \times (\alpha + 1)} \times m_1^U $$
Here, \(A_U\) is the rated current at discharge step \(U\), \(m_1\) and \(m_2\) are the initial and actual pulse rates, respectively, and \(\alpha\) is the internal resistance. The calculated terminal voltage was compared with the initial value to ensure errors remained within the controllable range of 0.02 V. Based on this, we determined the SOC estimation accuracy. The steady-state error \(H\) of SOC estimation was computed under discharge time backgrounds of 0.1 s, 0.3 s, and 0.5 s using the formula:
$$ H = \pi + \int (1 – \varphi^2 \times \frac{1}{Q}) \, d\varphi $$
where \(\pi\) is the pulse discharge initial value, \(\varphi\) is the discharge cycle, and \(Q\) is the convergence speed. The results from four test cycles are presented in the following table, showcasing the SOC estimation steady-state errors for each discharge time:
| SOC Estimation Cycle | Discharge Time 0.1 s: SOC Estimation Steady-State Error | Discharge Time 0.3 s: SOC Estimation Steady-State Error | Discharge Time 0.5 s: SOC Estimation Steady-State Error |
|---|---|---|---|
| Cycle 1 | 0.26 | 0.32 | 0.37 |
| Cycle 2 | 0.17 | 0.28 | 0.35 |
| Cycle 3 | 0.13 | 0.25 | 0.24 |
| Cycle 4 | 0.11 | 0.14 | 0.19 |
The data clearly demonstrate that across all test cycles and discharge times, the steady-state errors for SOC estimation of the LiFePO4 battery are consistently maintained below 0.4. This indicates high precision and robustness of our method. Moreover, the generalization ability of the estimation framework is significantly improved, as evidenced by the decreasing errors over successive cycles. The integration of compensation coefficients, multi-order observation equations, deep neural networks, and OCV correction collectively contributes to this enhanced performance. Compared to traditional SOC estimation techniques, our approach offers a more flexible and stable structure, effectively addressing limitations related to estimation range and unidirectional processing. By accounting for factors like battery nonlinearities, temperature variations, and aging effects, our method ensures reliable SOC estimates in diverse operational environments. This advancement not only optimizes the use and management of LiFePO4 batteries but also supports the broader adoption of electrochemical energy storage systems in renewable energy applications.
Further analysis reveals that the impedance characteristics of the LiFePO4 battery play a crucial role in SOC estimation. As shown in the impedance plot, the real part \(\text{Re}(Z)\) and imaginary part \(\text{Im}(Z)\) of the impedance vary with SOC, reflecting internal energy losses and kinetic processes. Our multi-order observation equation captures these variations by incorporating polarization voltages and state variables. The DNN model then leverages this information to predict SOC with high accuracy. The OCV correction step adds an additional layer of verification, aligning the estimates with empirical OCV-SOC relationships. This holistic approach minimizes errors caused by measurement noise, parameter drift, and environmental fluctuations. In practical applications, such as grid-scale energy storage, accurate SOC estimation for LiFePO4 batteries enables better scheduling, load balancing, and preventive maintenance. It also enhances safety by preventing operational extremes that could lead to thermal runaway or capacity degradation. Future work could explore the integration of adaptive algorithms to further improve real-time performance, or extend the method to other battery chemistries. Additionally, large-scale field tests could validate the method’s efficacy in real-world scenarios with varying load profiles and climatic conditions.
In conclusion, this research presents a comprehensive and effective method for SOC estimation of LiFePO4 batteries in electrochemical energy storage systems. By combining compensation coefficient calculation, multi-order observation equations, deep neural network modeling, and OCV verification correction, we achieve high-precision SOC estimates with steady-state errors below 0.4 across multiple test cycles. The method’s enhanced generalization and robustness make it suitable for diverse applications, contributing to improved battery management, extended lifespan, and optimized energy utilization. As the demand for renewable energy integration grows, advanced SOC estimation techniques like this will be instrumental in ensuring the reliability and efficiency of energy storage systems. The continuous evolution of such methods will further drive innovations in battery technology and sustainable energy infrastructure.