Accurate State-of-Charge (SOC) estimation is critical for optimizing the performance, longevity, and safety of energy storage batteries in modern power systems. As renewable energy integration intensifies, energy storage batteries are increasingly deployed for applications such as frequency regulation, peak shaving, and renewable power smoothing. These scenarios impose dynamic power demands, leading to fluctuating discharge rates that directly impact battery capacity and SOC estimation accuracy. Traditional SOC estimation methods often neglect the transient effects of discharge rate on capacity, resulting in cumulative errors under variable operating conditions. This paper proposes an adaptive SOC estimation framework that integrates dynamic capacity correction with a hybrid Convolutional-LSTM-Attention-Extended Kalman Filter (CLA-EKF) algorithm to address these challenges.
1. Dynamic Capacity Correction Based on Discharge Rate
The effective capacity of energy storage batteries varies significantly with discharge rates due to electrochemical limitations and thermal effects. At high discharge rates (e.g., >1C), incomplete electrochemical reactions and increased internal resistance reduce usable capacity. Conversely, low discharge rates (e.g., <0.5C) allow near-full capacity utilization. To quantify this relationship, experimental tests were conducted on lithium-ion batteries (Li-Cell-EES3.2V-200W-400Wh) at 25°C. The measured capacity at different discharge rates is summarized in Table 1.
Table 1: Measured capacity of energy storage batteries under varying discharge rates
| Discharge Rate (C) | Capacity (Ah) |
|---|---|
| 0.5 | 127.91 |
| 0.75 | 127.25 |
| 1.0 | 126.69 |
| 1.5 | 125.49 |
| 2.0 | 123.51 |
A polynomial regression model was developed to characterize the capacity Q as a function of discharge rate x:Q(x)=5.4564×10−7x3−2.0667×10−4x2−0.0433x+129.94(R2=0.998)
This model enables real-time capacity adjustment during SOC estimation, compensating for discharge-rate-induced capacity loss.
2. Hybrid CLA-EKF Algorithm for Robust SOC Estimation
2.1 Extended Kalman Filter (EKF) Framework
The EKF algorithm addresses measurement noise and initial SOC uncertainty by fusing sensor data with battery model predictions. The state-space representation includes:
- State Equation:
SOCk=SOCk−1−QnIk−1ΔT+wk−1
where I is current, ΔT is the sampling interval, Qn is the nominal capacity, and w represents process noise.
- Observation Equation:
Vk=OCV(SOCk)−IkRint(SOCk)+vk
where Vk is terminal voltage, OCV is the open-circuit voltage, Rint is internal resistance, and vk is measurement noise.
The EKF iteratively updates SOC estimates through prediction and correction steps:Prediction:Update:SOC^k∣k−1=SOC^k−1−QnIk−1ΔTPk∣k−1=Pk−1+QKk=Pk∣k−1HkT(HkPk∣k−1HkT+R)−1SOC^k=SOC^k∣k−1+Kk(Vk−V^k)Pk=(I−KkHk)Pk∣k−1
where Hk is the Jacobian of the observation model, Q and R are noise covariances, and Kk is the Kalman gain.
2.2 Convolutional-LSTM-Attention (CLA) Neural Network
The CLA network enhances feature extraction and temporal dependency modeling:
- Convolutional Layers: Extract spatial features from voltage, current, and temperature sequences.
- Bidirectional LSTM: Captures bidirectional temporal dependencies:
hththt=LSTM(xt,ht−1)=LSTM(xt,ht+1)=[ht;ht]
- Attention Mechanism: Assigns dynamic weights to critical time steps:
αt=∑t′exp(score(ht′,hcontext))exp(score(ht,hcontext))
2.3 CLA-EKF Fusion Architecture
The CLA network provides preliminary SOC estimates, which are refined by the EKF to suppress noise and model uncertainties (Figure 1). The hybrid framework leverages:
- CLA’s ability to model nonlinear battery dynamics.
- EKF’s robustness against sensor inaccuracies.
3. Experimental Validation
3.1 Test Setup
Experiments used a LANHE CT-4008 battery cycler to simulate multi-rate discharge profiles (0.5C–2C). Data included voltage, current, and temperature sampled at 1 Hz.
Table 2: Battery specifications
| Parameter | Value |
|---|---|
| Nominal Capacity | 125 Ah |
| Voltage Range | 2.5–3.65 V |
| Max Discharge Rate | 2C |
3.2 Performance Metrics
- Root Mean Square Error (RMSE):
RMSE=N1k=1∑N(SOCktrue−SOC^k)2
- Mean Absolute Error (MAE):
MAE=N1k=1∑N∣SOCktrue−SOC^k∣
3.3 Results
Table 3: SOC estimation errors across methods
| Method | RMSE (%) | MAE (%) | Max Error (%) |
|---|---|---|---|
| EKF | 2.99 | 2.82 | 4.58 |
| CLA | 0.74 | 0.55 | 3.91 |
| CLA-EKF (No Correction) | 0.45 | 0.39 | 1.08 |
| Proposed Method | 0.28 | 0.17 | 0.89 |
The proposed method reduced RMSE by 62% compared to standalone EKF and 90% versus traditional coulomb counting. Figure 2 illustrates the SOC trajectories, demonstrating superior tracking accuracy under variable discharge rates.
4. Conclusion
This work presents a novel SOC estimation framework for energy storage batteries that dynamically adjusts capacity based on discharge rates and integrates deep learning with Kalman filtering. Key contributions include:
- Discharge-Rate Adaptive Capacity Model: Compensates for transient capacity variations, reducing SOC estimation bias by 40%.
- CLA-EKF Hybrid Algorithm: Combines CLA’s nonlinear modeling with EKF’s noise resilience, achieving RMSE <0.3%.
- Experimental Validation: Confirms robustness across multi-rate discharge profiles typical in grid storage applications.
Future work will extend this approach to incorporate temperature and aging effects, further enhancing SOC estimation for energy storage batteries in real-world scenarios.