As renewable energy applications expand, the battery energy storage system plays an increasingly critical role in balancing energy supply and demand and improving energy efficiency. Lithium iron phosphate batteries, known for their high energy density, long cycle life, and environmental friendliness, are widely used in electrochemical energy storage systems. Accurate state of charge estimation is a key component of battery energy storage system management, as it ensures battery safety, prolongs battery life, and enhances energy utilization efficiency. Traditional estimation methods for lithium iron phosphate batteries often rely on periodic or fixed-interval measurements, which suffer from limited coverage and lead to significant estimation errors. Additionally, conventional approaches typically adopt a unidirectional estimation structure with low efficiency, further degrading the accuracy of SOC estimation. To address these challenges, we propose a novel method for SOC estimation of lithium iron phosphate batteries in battery energy storage systems. Our approach integrates multi-order observation equations, a deep neural network model, and open circuit voltage verification correction to achieve robust and precise estimation under diverse operating conditions.
In this study, we first calculate the compensation coefficient for SOC estimation to account for nonlinear battery dynamics, inconsistent charge-discharge conditions, and aging effects. Then, we establish a multi-order observation equation to extend the estimation range and improve adaptability. Based on this, we design a deep neural network model that leverages voltage, current, and temperature data to estimate the battery state. Finally, we apply OCV verification correction to refine the results, ensuring high accuracy under varying environmental and aging conditions. The proposed method is validated through extensive experiments, and the results demonstrate that the steady-state estimation error is consistently below 0.4, indicating strong generalization capability and practical applicability in battery energy storage systems.
1. Methodology for SOC Estimation in Battery Energy Storage Systems
1.1 Calculation of SOC Compensation Coefficient and Multi-Order Observation Equation
The operation of lithium iron phosphate batteries is complex, and accurate SOC estimation requires careful consideration of various factors. We begin by establishing the recursive relationship for the battery SOC, which can be expressed as:
$$
SOC(k) = SOC(k-1) + \frac{\Delta \iota_1 (k-1) \chi}{\iota_2}
$$
where \( SOC(k) \) represents the battery charge recursion, \( k \) denotes the recursion index, \( \iota_1 \) and \( \iota_2 \) represent the initial and actual charge values respectively, and \( \chi \) is the battery operating frequency. Using this recursion, we define an exponential function within the ratio range of capacity at different discharge rates to the capacity at 1C discharge, enabling a recursive fitting process. The compensation coefficient is then calculated as:
$$
B = o^2 – \sum_{z=1}^{n} \vartheta_z + \gamma
$$
where \( B \) is the compensation coefficient, \( o \) is the battery health factor, \( \vartheta \) is the average capacity, \( z \) indicates battery temperature, and \( \gamma \) represents the number of charge-discharge cycles. With the determined compensation coefficient, we further design a multi-order observation equation to capture the dynamic behavior of the battery:
$$
\begin{bmatrix}
D_j(g) \\
D_w(g) \\
SOC(k)
\end{bmatrix}
=
\begin{bmatrix}
e^{\Delta f – \partial} & 0 & 0 \\
0 & e + \frac{1}{\Delta f – \partial} & 0 \\
0 & 0 & 1
\end{bmatrix}
\begin{bmatrix}
D_j(g-1) \\
D_w(g-1) \\
SOC(k-1)
\end{bmatrix}
$$
Here, \( D_j(g) \) and \( D_w(g) \) denote polarization voltages, \( SOC(k) \) is the state variable, \( \Delta f \) is the temperature variation, \( \partial \) is the input vector, and \( e \) is the output vector. This multi-order equation allows us to comprehensively observe the battery’s operating status and SOC over multiple cycles, providing a solid foundation for subsequent estimation.
1.2 Design of the Deep Neural Network SOC Estimation Model
We integrate a deep neural network architecture to build an SOC estimation model that leverages voltage, current, and temperature measurements. At different frequencies, small-amplitude sinusoidal current signals induce AC impedance, which correlates with the SOC. Using the constructed observation equation, we analyze the impedance characteristics, as shown in the following figure.
The impedance characteristic plot reveals that the real part of impedance \( Re(Z) \) reflects internal resistance and energy loss, while the imaginary part \( Im(Z) \) represents the dynamic electrode reaction and electrolyte capacitance. Under the deep neural network framework, we collect voltage and current data over a given period. The flow of the model is systematic: data acquisition, preprocessing, feature extraction, and SOC regression. The SOC estimate from the model is given by:
$$
\xi = (1 – \zeta^2) \times \upsilon
$$
where \( \xi \) is the model SOC estimation, \( \zeta \) is the impedance characteristic value, and \( \upsilon \) is the current difference. The deep neural network is trained to map these features to the true SOC, enabling accurate state estimation across various operating profiles relevant to battery energy storage systems.
1.3 OCV Verification Correction for State Estimation
Open circuit voltage verification correction is a widely used method for refining SOC estimates based on the known relationship between OCV and SOC. Our approach involves measuring the battery’s open circuit voltage and establishing the OCV-SOC mapping, while compensating for factors such as temperature and aging. The correction process is sequential: we first measure OCV, then apply temperature compensation and aging compensation to eliminate deviations. The corrected OCV is then compared with the model output to validate and adjust the SOC estimate. This step significantly enhances estimation accuracy, especially in long-term operation of battery energy storage systems where aging effects are pronounced.
2. Experimental Validation and Discussion
2.1 Test Setup
To verify the effectiveness of the proposed method, we conducted experiments using a MATLAB-based simulation platform. The battery energy storage system was configured with a lithium iron phosphate battery pack having a rated capacity of 25 Ah, a cutoff voltage upper limit of 4.25 V and lower limit of 2.16 V, a sampling frequency of 1.25 Hz, and an ambient temperature of 25 °C. The test duration spanned four cycles, and the auxiliary test parameters are listed in Table 1.
| Parameter | Value |
|---|---|
| Open circuit voltage / V | 6.5 |
| Constant current discharge / A | 10–12 |
| Static capacity / Ah | 20–28 |
| Ambient temperature variation / °C | 18–25 |
We connected sensing and data acquisition devices to the battery control system to capture real-time voltage and current data. The battery was subjected to a 50 C standard pulse discharge at 25 °C, with a discharge interval of 0.3 to 0.5 seconds. Each pulse cycle was set to 0.1 seconds, and the corresponding voltage and current data were collected.
2.2 Test Results
During the pulse discharge, we measured the terminal voltage under different resistance conditions. The terminal voltage was calculated using the following formula:
$$
F = \sum_{U=1}^{n} \frac{A_U – m_2^2}{m_1 \times (\alpha + 1)} \times m_1 U
$$
where \( F \) is the terminal voltage, \( A \) is the rated current, \( U \) is the discharge index, \( m_1 \) and \( m_2 \) are the initial and actual pulse rates respectively, and \( \alpha \) is the internal resistance. The error between the initial and current terminal voltages was controlled within 0.02 V. Then, we computed the SOC estimation steady-state error using:
$$
H = \pi + \int \left(1 – \phi^2 \times \frac{1}{Q}\right)
$$
where \( H \) is the steady-state error, \( \pi \) is the initial pulse discharge value, \( \phi \) is the discharge period, and \( Q \) is the convergence speed. The results across four test cycles and three discharge time points are summarized in Table 2.
| Cycle | Error at 0.1 s | Error at 0.3 s | Error at 0.5 s |
|---|---|---|---|
| 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 in Table 2 clearly indicate that the proposed method consistently maintains the steady-state estimation error below 0.4 across all cycles and discharge times. The error decreases as the test proceeds, demonstrating good convergence and generalization ability. Compared to traditional approaches, our method achieves higher efficiency and precision, making it well-suited for real-world applications in battery energy storage systems.
3. Conclusion
In this work, we developed a comprehensive SOC estimation method for lithium iron phosphate batteries within battery energy storage systems. By integrating compensation coefficient calculation, multi-order observation equations, deep neural network modeling, and OCV verification correction, we significantly improved estimation accuracy and robustness. The experimental results confirm that the steady-state error remains below 0.4, verifying the method’s effectiveness in handling nonlinear electrochemical characteristics, aging effects, and varying operating conditions. This approach enhances the reliability and efficiency of battery energy storage system management, paving the way for more intelligent energy storage applications.