In modern power systems, the rapid integration of renewable energy sources has intensified grid volatility, making energy storage batteries a critical component for stabilizing supply, managing peak demands, and ensuring frequency regulation. The state of charge (SOC) of an energy storage battery serves as a fundamental indicator of its remaining energy capacity, directly influencing operational efficiency, lifespan, and safety. Accurate SOC estimation is therefore paramount for optimizing the performance of energy storage systems across diverse applications, from short-duration high-power responses to long-duration energy shifting. Traditional SOC estimation methods, such as coulomb counting and model-based filters, often struggle under variable operating conditions, particularly when discharge rates fluctuate. These fluctuations significantly impact the actual usable capacity of the energy storage battery, leading to estimation inaccuracies that can compromise system reliability. This work addresses this challenge by proposing a novel SOC estimation framework that dynamically corrects battery capacity based on the instantaneous discharge rate and leverages an advanced hybrid algorithm combining deep learning with Kalman filtering.
Our core contribution is a comprehensive method that enhances SOC estimation accuracy for energy storage batteries operating in multi-scenario grid environments. We first analyze the intrinsic error mechanisms in conventional approaches, highlighting how neglecting discharge-rate-dependent capacity variations introduces significant偏差. We then establish a quantitative model characterizing the relationship between discharge current and effective capacity. Building on this, we develop a hybrid estimator named CLA-EKF, which fuses a Convolutional Long Short-term memory Attention neural network (CLA) with an Extended Kalman Filter (EKF). This synergy harnesses the nonlinear mapping prowess of deep learning and the noise-resilient, recursive correction capability of the Kalman filter. Finally, we integrate a real-time, discharge-rate-aware capacity adaptation module into this estimator. Experimental validation demonstrates that our proposed method achieves superior precision and robustness compared to standard techniques under complex, variable-power profiles typical of grid-connected energy storage battery operations.
The foundation of most SOC estimation techniques lies in the definition provided by the ampere-hour (or coulomb counting) integral method. For an energy storage battery, the SOC at time \( t \) is given by:
$$SOC(t) = SOC(0) – \frac{1}{Q_n} \int_0^t I(\tau) d\tau$$
where \( SOC(0) \) is the initial state of charge, \( I(t) \) is the instantaneous current (positive for discharge), and \( Q_n \) is the nominal or rated capacity of the battery. The primary error sources stemming from this definition are threefold: measurement inaccuracies in current sensing, uncertainty in the initial SOC value, and, most critically for this work, the assumption that \( Q_n \) is a constant. In reality, the effective capacity \( Q_{eff} \) of an energy storage battery is not fixed; it is a function of several factors, with discharge rate (C-rate) and temperature being the most prominent. For grid-scale energy storage systems operating in controlled environments, ambient temperature is often relatively stable, making the discharge rate the dominant variable affecting short-term capacity. Higher discharge rates accelerate internal chemical reactions and increase ohmic losses, leading to a reduction in the total extractable energy before the voltage reaches the cutoff threshold. Ignoring this dynamic effectively means using an incorrect divisor in the SOC integral, causing the estimated SOC to deviate from its true value. This error accumulates over time and can be substantial during operations involving frequent power ramping, which is common for energy storage batteries providing services like frequency regulation or solar smoothing.
To quantify this relationship, we conducted experimental characterization on a commercial lithium iron phosphate (LFP) energy storage battery cell. The battery was tested at a constant ambient temperature of 25°C under various constant-current discharge rates. The measured effective capacities are summarized in Table 1.
| Discharge Rate (C) | Measured Effective Capacity (Ah) |
|---|---|
| 0.5C | 127.91 |
| 0.75C | 127.25 |
| 1.0C | 126.69 |
| 1.5C | 125.49 |
| 2.0C | 123.51 |
The data clearly shows a monotonic decrease in capacity with increasing discharge rate. We fitted a polynomial model to this data to establish a continuous function for dynamic capacity correction. The derived relationship between discharge current \( I \) (in Amperes, where 1C corresponds to the nominal current for 1-hour discharge) and the effective capacity \( Q_{eff}(I) \) is:
$$Q_{eff}(I) = aI^3 + bI^2 + cI + d$$
Using regression analysis, the coefficients were determined as: \( a = 5.4564 \times 10^{-7} \), \( b = 2.0667 \times 10^{-4} \), \( c = 0.0433 \), and \( d = 129.9400 \). Therefore, the capacity-aware SOC update equation becomes:
$$SOC(t) = SOC(t-1) – \frac{I(t-1) \Delta T}{Q_{eff}(I(t-1))} + w_{t-1}$$
where \( \Delta T \) is the sampling interval and \( w \) represents process noise. This model replaces the constant \( Q_n \) in the standard EKF state transition equation, allowing the estimator to adapt its “understanding” of total capacity based on the real-time operating current of the energy storage battery.
While dynamic capacity correction addresses one major error source, achieving high estimation accuracy also requires a robust algorithm to handle nonlinear battery dynamics, model uncertainties, and sensor noise. We propose a hybrid architecture, the CLA-EKF estimator, which combines the strengths of data-driven deep learning and model-based stochastic filtering. The CLA neural network is designed to learn the complex, temporal relationship between measurable battery parameters (terminal voltage, current, temperature) and the SOC. Its structure is as follows: 1) A one-dimensional convolutional layer extracts local, high-level features from the input time-series data. 2) A bidirectional Long Short-Term Memory (Bi-LSTM) layer captures long-range temporal dependencies in both forward and backward directions, crucial for understanding the hysteresis and relaxation effects in energy storage batteries. 3) An attention mechanism is applied to the Bi-LSTM outputs, assigning adaptive weights to different time steps to emphasize the most informative features for SOC estimation. 4) Finally, fully connected layers map the weighted features to a single SOC output. The network is trained offline on historical operational data from the energy storage battery, learning a powerful nonlinear mapping function \( f_{CLA} \):
$$\widehat{SOC}_{CLA}(t) = f_{CLA}(V(t), I(t), T(t), …)$$
where \( V, I, T \) are voltage, current, and temperature, respectively.
However, a purely data-driven model like CLA can be sensitive to unseen noise patterns and distribution shifts. To enhance robustness and enable online recursive correction, we integrate its output with an Extended Kalman Filter (EKF). The EKF provides an optimal estimation framework for nonlinear systems by linearizing the state-space model around the current estimate. In our hybrid setup, the EKF’s state vector is the SOC, and the measurement is the SOC predicted by the CLA network. The state transition incorporates the capacity-corrected ampere-hour integration. The discrete-time state-space model for the EKF is defined as:
State Transition (Process) Equation:
$$x_k = x_{k-1} – \frac{I_{k-1} \Delta T}{Q_{eff}(I_{k-1})} + w_{k-1}, \quad x_k = SOC_k$$
Measurement Equation:
$$z_k = x_k + v_k, \quad z_k = \widehat{SOC}_{CLA, k}$$
Here, \( w_k \) and \( v_k \) are zero-mean Gaussian process and measurement noise with covariances \( Q \) and \( R \), respectively. The EKF algorithm then proceeds through its standard prediction and update cycles:
1. Initialization:
$$ \hat{x}_{0|0} = E[x_0], \quad P_{0|0} = E[(x_0 – \hat{x}_{0|0})(x_0 – \hat{x}_{0|0})^T] $$
2. Prediction Step:
$$ \hat{x}_{k|k-1} = \hat{x}_{k-1|k-1} – \frac{I_{k-1} \Delta T}{Q_{eff}(I_{k-1})} $$
$$ P_{k|k-1} = P_{k-1|k-1} + Q $$
(Note: The state transition Jacobian \( A_k \) is 1 in this scalar case).
3. Update Step:
$$ K_k = P_{k|k-1} (P_{k|k-1} + R)^{-1} $$
$$ \hat{x}_{k|k} = \hat{x}_{k|k-1} + K_k (z_k – \hat{x}_{k|k-1}) $$
$$ P_{k|k} = (1 – K_k) P_{k|k-1} $$
The Kalman gain \( K_k \) optimally blends the model-based prediction (corrected with dynamic capacity) and the CLA network’s measurement. This fusion makes the overall estimator highly resilient to initial SOC errors, current sensor drift, and transient disturbances, while fully accounting for the discharge-rate effect on the energy storage battery’s capacity.
To validate the proposed method, we designed a comprehensive experimental campaign emulating a grid-support operational profile for an energy storage battery. The test involved a sequence of constant-current discharge phases at different rates, mimicking a scenario where the battery responds to varying power demands: 2C for 10 minutes, then 1.5C, 1C, 0.75C, each for 10 minutes, followed by a 0.5C discharge until the voltage cutoff. Voltage and current were sampled at a high frequency. We implemented several estimators for comparison: the standard EKF (with constant capacity), the EKF with dynamic capacity correction (EKF-DC), the standalone CLA network, a hybrid LSTM-EKF, our proposed CLA-EKF (without capacity correction), and the full proposed method (CLA-EKF with dynamic capacity correction). Performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Maximum Error (ME) against a reference SOC derived from high-precision laboratory equipment.
The results conclusively demonstrate the advantages of each component of our approach. First, the impact of dynamic capacity correction alone is significant. Table 2 compares the standard EKF and the EKF-DC.
| Method | RMSE (%) | MAE (%) | ME (%) |
|---|---|---|---|
| Standard EKF | 2.9937 | 2.8248 | 4.5807 |
| EKF with Capacity Correction (EKF-DC) | 1.7728 | 1.5576 | 3.0820 |
The error metrics show a reduction of approximately 40% in RMSE and 45% in MAE, proving that adapting the capacity model to the discharge rate is crucial for accurate SOC tracking in an energy storage battery under variable load.
Next, we evaluate the algorithmic advancement of the CLA-EKF hybrid over other data-driven and hybrid methods. Table 3 presents the error metrics for four different algorithms (all using constant nominal capacity for a controlled comparison).
| Method | RMSE (%) | MAE (%) | ME (%) |
|---|---|---|---|
| Standard EKF | 2.9937 | 2.8248 | 4.5807 |
| Standalone CLA Network | 0.7433 | 0.5523 | 3.9093 |
| LSTM-EKF Hybrid | 1.1992 | 1.0373 | 3.8048 |
| Proposed CLA-EKF (without cap. correction) | 0.4498 | 0.3859 | 1.0796 |
The standalone CLA network already outperforms the model-based EKF significantly, highlighting the power of deep learning for modeling energy storage battery dynamics. The hybrid methods (LSTM-EKF and CLA-EKF) further improve performance by filtering out noise. Our CLA-EKF, with its attention-enhanced feature extraction, achieves the best results among these, with an RMSE of only 0.4498%, demonstrating the effectiveness of the chosen neural architecture within the filtering framework.
Finally, we integrate the two key innovations: the CLA-EKF algorithm and the dynamic capacity correction. The performance of this complete proposed method is compared against the strongest baselines in Table 4.
| Method | RMSE (%) | MAE (%) | ME (%) |
|---|---|---|---|
| EKF with Capacity Correction (EKF-DC) | 1.7728 | 1.5576 | 3.0820 |
| CLA-EKF (without capacity correction) | 0.4498 | 0.3859 | 1.0796 |
| Full Proposed Method (CLA-EKF with Capacity Correction) | 0.2769 | 0.1722 | 0.8980 |
The synergy is clear. The full proposed method achieves the lowest error across all metrics, with an RMSE of 0.2769%, representing an overall accuracy improvement of over 90% compared to the standard EKF. The error trajectory over time for this method remains tightly bounded near zero, even during the abrupt transitions between discharge rates, showcasing exceptional stability and precision. This level of accuracy is vital for advanced energy management systems that rely on precise SOC information to make decisions about power dispatch, health assessment, and safety protocols for large-scale energy storage battery installations.
The proposed framework’s mathematical consistency can be further analyzed by examining the error covariance propagation. The EKF’s update step minimizes the a posteriori error covariance \( P_{k|k} \), which, for our scalar SOC case, simplifies to \( P_{k|k} = (1 – K_k)P_{k|k-1} \). The Kalman gain is calculated as \( K_k = P_{k|k-1}/(P_{k|k-1} + R) \). The measurement noise covariance \( R \) here essentially represents the uncertainty in the CLA network’s prediction. By training the CLA network on comprehensive data, we can reduce its inherent variance, leading to a smaller effective \( R \). This, in turn, increases the Kalman gain, allowing the filter to place more weight on the accurate neural network measurement, thereby accelerating error correction. Simultaneously, the process noise covariance \( Q \) accounts for uncertainties in the state transition model, including any residual errors from the capacity correction function \( Q_{eff}(I) \). The adaptive nature of \( Q_{eff}(I) \) inherently reduces the systematic error in the state prediction, resulting in a better initial prediction \( \hat{x}_{k|k-1} \) before the update. The combined effect is a rapid convergence and sustained accuracy of the SOC estimate for the energy storage battery.
In conclusion, this work presents a significant advancement in SOC estimation for grid-connected energy storage batteries. We have identified and systematically addressed a key practical issue—the dynamic variation of usable capacity with discharge rate—which is often overlooked in academic and industrial battery management systems. By developing a polynomial-based capacity adaptation model and embedding it within a sophisticated CLA-EKF hybrid estimator, we create a robust, accurate, and adaptive SOC estimation solution. The method successfully marries the high representational capacity of deep learning for complex electrochemical dynamics with the optimal recursive estimation and noise suppression properties of the Kalman filter, all while dynamically adjusting to the real-time operating conditions of the energy storage battery. Experimental results under a demanding variable discharge rate profile confirm its superior performance over conventional and state-of-the-art methods. This approach provides a reliable foundation for enhancing the operational efficiency, longevity, and safety of energy storage systems, facilitating their broader integration into the future smart grid. Future work will focus on extending this framework to account for additional real-world complexities such as temperature gradients, aging effects across the entire lifespan of the energy storage battery, and the challenges of SOC estimation for heterogeneous battery packs in large-scale installations.