With the increasing integration of renewable energy sources, accurate state-of-charge (SOC) estimation for energy storage batteries has become critical for ensuring grid stability and optimizing power dispatch. This paper presents a novel SOC estimation methodology that addresses capacity variations induced by dynamic discharge rates in multi-scenario grid applications.
1. Capacity-Discharge Rate Characterization
The fundamental relationship between discharge rate (C-rate) and effective capacity is established through experimental analysis. For a 125Ah lithium iron phosphate (LFP) energy storage battery at 25°C, capacity measurements reveal nonlinear degradation patterns:
$$Q(I) = 5.4564 \times 10^{-7}I^3 – 2.0667 \times 10^{-4}I^2 + 0.0433I + 129.94$$
| C-rate | Capacity (Ah) | Deviation (%) |
|---|---|---|
| 0.5C | 127.91 | +2.33 |
| 1.0C | 126.69 | +1.35 |
| 2.0C | 123.51 | -1.19 |
This capacity model enables real-time adjustment of the energy storage battery’s effective capacity based on operational C-rate, significantly improving SOC estimation accuracy under variable power demands.
2. Hybrid CLA-EKF Estimation Framework
The proposed architecture combines convolutional-LSTM attention networks (CLA) with extended Kalman filtering (EKF) for robust SOC estimation:
$$x_k = f(x_{k-1}, u_{k-1}) + w_{k-1}$$
$$z_k = h(x_k) + v_k$$
Where the state vector \( x_k \) contains SOC and polarization voltages, with measurement vector \( z_k \) including terminal voltage and temperature. The CLA network processes temporal patterns through:
$$h_t = \text{LSTM}(W_h[h_{t-1}, x_t] + b_h)$$
$$a_t = \text{softmax}(W_a h_t + b_a)$$
$$c_t = \sum_{i=1}^T a_i h_i$$
Key algorithm components:
| Module | Function | Parameters |
|---|---|---|
| CLA Network | Nonlinear mapping | 3 Conv layers, 128 LSTM units |
| EKF Corrector | Noise suppression | Q=1e-5, R=1e-3 |
| Capacity Adaptor | Real-time adjustment | 5th-order polynomial |
3. Experimental Validation
Testing under variable C-rate conditions (0.5C-2C) demonstrates the method’s superiority:
$$RMSE = \sqrt{\frac{1}{N}\sum_{k=1}^N (SOC_{true} – SOC_{est})^2$$
| Method | RMSE (%) | MAE (%) | Max Error (%) |
|---|---|---|---|
| Standard EKF | 2.99 | 2.82 | 4.58 |
| CLA Only | 0.74 | 0.55 | 3.91 |
| Proposed Method | 0.28 | 0.17 | 0.89 |
The capacity-adaptive CLA-EKF achieves 62.5% lower RMSE compared to conventional EKF, demonstrating exceptional performance in energy storage battery management scenarios.
4. Thermal-Capacity Coupling Analysis
While focusing on C-rate effects, the framework can be extended to include thermal dynamics:
$$Q(T,I) = Q_{25^{\circ}\text{C}}(I) \times [1 + \alpha(T-25)]$$
Where \( \alpha \) represents the temperature coefficient (typically 0.002-0.005°C⁻¹ for LFP energy storage batteries). This extension enables comprehensive SOC estimation across operational environments.
5. Conclusion
This work advances energy storage battery management through three key contributions: 1) C-rate dependent capacity modeling, 2) Hybrid CLA-EKF estimation architecture, and 3) Real-time adaptive SOC correction. The methodology demonstrates <1% estimation error under realistic grid operating conditions, significantly enhancing the reliability of energy storage systems in renewable integration scenarios.
$$SOC_{final} = SOC_{EKF} \times (1 – \lambda) + SOC_{CLA} \times \lambda$$
With \( \lambda \) dynamically adjusted between 0.6-0.8 based on operating conditions, the algorithm optimally balances model-based and data-driven approaches for energy storage battery state estimation.