In the context of global energy transition and sustainable development, the optimization of energy structures and the innovation of smart grid technologies have become crucial driving forces for social progress. As a key component for balancing grid supply and demand and improving energy utilization efficiency, energy storage systems have gained increasing importance. Among various battery chemistries, lithium iron phosphate (LFP) batteries, known for their excellent safety and long cycle life, are widely applied in smart grids, residential energy storage, and electric vehicles. However, with the expansion of application scenarios, safety concerns related to energy storage battery systems remain prominent. The stress induced by structural constraints within battery modules has emerged as a critical factor affecting battery performance and safety. During charge and discharge cycles, internal stress not only may cause structural deformation but also potentially lead to safety incidents. Therefore, it is essential to deeply investigate the stress characteristics of LFP batteries, explore the intrinsic relationship between stress variations and battery states, and develop state estimation algorithms that integrate both stress and electrical parameters. This work provides a theoretical foundation for digital twin modeling and safety management of energy storage batteries.
The voltage plateaus of both the positive and negative electrodes of LFP batteries are relatively wide. Given the limited accuracy of voltage sensors in battery management systems, it becomes difficult to correct the state of charge (SOC) when the battery operates within these plateau regions. Moreover, the current in energy storage systems tends to be stable, making model parameters challenging to observe, which further complicates SOC estimation. Since SOC cannot be measured directly by sensors, it must be estimated through physical quantities such as current, voltage, temperature, and stress. Researchers worldwide have conducted extensive studies on SOC estimation methods for lithium-ion batteries. Common approaches include the ampere-hour integration method, open-circuit voltage method, model-based filtering methods, and machine learning methods. The ampere-hour integration method is the most basic, integrating current over time to estimate capacity, but it is an open-loop method sensitive to initial SOC accuracy and current measurement errors. The open-circuit voltage method relies on the stable relationship between OCV and SOC, but the wide voltage plateau of LFP batteries reduces its reliability. To overcome these limitations, model-based methods combining equivalent circuit models or electrochemical models with filtering algorithms such as Kalman filters have been developed. Extended Kalman filter, unscented Kalman filter, and cubature Kalman filter have been widely applied for nonlinear battery systems. With the advancement of computational techniques, data-driven approaches, including machine learning and deep learning, have become research hotspots, establishing mapping relationships between collected data and SOC.
Recent studies have highlighted the role of stress characteristics in battery state optimization and evaluation. Appropriate compressive stress can improve contact between electrodes and electrolyte, enhancing battery performance. In battery module assembly, pre-stress is often set at hundreds of kilograms. The stress varies with battery SOC, providing a new information dimension for state estimation. Considering the complex electrochemical reactions and multiple influencing factors, methods based on a single physical field often fail to achieve high accuracy. Multi-parameter fusion techniques have thus become a trend in SOC estimation. Digital twin technology for energy storage systems constructs virtual mapping models of physical entities, enabling real-time multi-source data collection and supporting state estimation. By integrating electrical, thermal, and stress data, digital twins can further improve estimation accuracy through virtual-real interaction.
In this study, we focus on stress characteristic analysis and deep neural network-based state estimation for LFP energy storage batteries. To address the challenge of long voltage plateaus and small voltage variations that hinder traditional SOC estimation, we conduct stress characteristic experiments under different charge/discharge rates and pre-stress conditions. We design a CNN-BiLSTM model tailored for constant-current/constant-power application scenarios of LFP energy storage batteries. The effectiveness of the proposed method is verified through experiments, combining stress characteristics with machine learning to provide a new technical pathway for state estimation and safety management.
1. Methodology
1.1 Stress Characteristics of LFP Batteries
During charging and discharging, the positive and negative electrodes undergo lithium extraction or insertion reactions, causing structural changes. Without external constraints, the battery thickness would vary accordingly. In energy storage battery modules, physical constraints convert these dimensional changes into measurable stress. Studies show that the positive electrode of LFP batteries exhibits a nearly linear volume decrease of about 7% during charging, while the graphite negative electrode shows a non-monotonic thickness increase of about 8%. The combined thickness change of the cell is non-monotonic. When external mechanical constraints exist, the surface stress during charging also exhibits non-monotonic behavior, generally increasing overall. During discharging, stress similarly shows non-monotonic decreasing trends. The relationship among electrode thickness, stress, and SOC is illustrated in the conceptual relationship (Figure 1).
From the above relationship, it is clear that stress and SOC have a relatively stable mapping, making stress data valuable for state estimation when combined with other parameters.
1.2 Data Preprocessing
Data collected from different terminals in battery experiments often have slight timestamp discrepancies. We align the timestamps accurately, removing start-up, shutdown, and idle data to ensure precision. Since experiments include sequential charging, resting, and discharging steps, we segment and preprocess the data, discarding rest intervals and extracting continuous charge/discharge sequences. After alignment and truncation, we obtain a unified dataset containing SOC, current, voltage, temperature, and stress. To enhance features, we compute differential charge ($\Delta Q$) and differential stress ($\Delta F$). Anomalies are removed using the 3-sigma criterion, and moving average filtering is applied to smooth random noise, yielding a clean dataset for model training.
1.3 CNN-BiLSTM Model Architecture
When designing SOC estimation for LFP batteries, we consider that SOC depends not only on instantaneous current but also on historical states. Historical voltage, current, and stress data, along with their evolution trends, contribute to better estimation. Hence, we construct a CNN-BiLSTM model that fuses stress and electrical parameters. The CNN effectively extracts local features from multi-dimensional data, addressing the instability caused by the wide voltage plateau, especially in the middle SOC range (40%–90%). Combined with stress features, CNN enhances the distinguishability of similar voltage values at different SOC levels. The BiLSTM incorporates bidirectional temporal processing by using forward and backward LSTM networks to capture past and future dependencies. The gating mechanisms (forget gate, input gate, output gate) are defined as follows:
$$ f_t = \sigma(W_f [h_{t-1}, x_t] + b_f) $$
$$ \tilde{C}_t = \tanh(W_c [h_{t-1}, x_t] + b_c) $$
$$ i_t = \sigma(W_i [h_{t-1}, x_t] + b_i) $$
$$ C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t $$
$$ o_t = \sigma(W_o [h_{t-1}, x_t] + b_o) $$
$$ h_t = o_t \odot \tanh(C_t) $$
The BiLSTM concatenates the hidden states from both directions to capture richer temporal information. Our CNN-BiLSTM model accepts six input features: $\Delta Q$, $\Delta F$, voltage $V$, current $I$, stress $F$, and temperature $T$. The model architecture is summarized in Table 1.
| Layer | Details |
|---|---|
| Input | 6 features: $\Delta Q$, $\Delta F$, $V$, $I$, $F$, $T$ (sequence length variable) |
| 1D-CNN | Kernel size: 3×1, 64 filters, ReLU activation, followed by max-pooling |
| BiLSTM | 2 layers, 128 units per direction (256 concatenated), dropout 0.3 |
| Dense | Fully connected layer, 64 neurons, ReLU |
| Output | 1 neuron, linear activation, SOC estimate |
All input features and the target SOC are normalized to [0,1] using min-max scaling. Training uses mean squared error (MSE) loss and Adam optimizer with initial learning rate 0.001, momentum 0.9. Gradient clipping at 5.0 is applied. The dataset is split into training (60%), validation (20%), and test (20%) sets. Batch size is 64, and training runs for 200 epochs with early stopping based on validation loss.
1.4 SOC Estimation Procedure
We train separate models for charging and discharging. After training, we evaluate on full-cycle test data and also on partial data (SOC 60%–90% for charging, 40%–90% for discharging) to assess robustness under non-full-cycle conditions.
2. Experimental Details
2.1 Battery Specifications and Test Setup
We used commercial LFP pouch cells (model GSP7514238, Guangzhou Penghui Energy) with parameters listed in Table 2.
| Parameter | Value |
|---|---|
| Nominal Capacity | 25 Ah |
| Nominal Voltage | 3.2 V |
| Dimensions | 238.0 × 140.0 × 7.6 mm |
| Max Charge Rate | 1 C |
| Max Discharge Rate | 2 C |
| Charge Cut-off Voltage | 3.65 V |
| Discharge Cut-off Voltage | 2.5 V |
The experimental setup consisted of a steel fixture with a load cell to measure pre-stress and dynamic stress. Two battery samples were tested simultaneously. A multi-channel data acquisition system (Rigol M300) recorded stress and temperature at 10 s intervals, while voltage and current were recorded by a battery cycler at 1 s intervals.
2.2 Test Procedure
The tests were conducted at room temperature. The procedure is outlined in Table 3.
| Step | Description |
|---|---|
| 1 | Apply 500 kg pre-stress to both cells |
| 2 | Perform characterization at 0.1C, 0.5C, 1C for rate analysis |
| 3 | Constant current (1C) charge to 3.65 V |
| 4 | Rest 1 hour |
| 5 | Constant current (1.5C) discharge to 2.5 V |
| 6 | Rest 1 hour |
| 7 | Repeat steps 3–6 for 40 cycles |
| 8 | End |
3. Results and Discussion
3.1 Analysis of Electrical and Stress Data
Figure 2 (not shown) illustrates typical voltage and stress profiles over one cycle. The voltage plateau is evident in the middle of charge and discharge, making SOC estimation challenging. Stress varies by about 35 kg (from ~495 kg to ~530 kg) and exhibits non-monotonic behavior in the middle SOC range, providing additional information. Over 40 cycles, stress gradually decreased initially and stabilized after cycle 10. Therefore, we used cycles 10–30 for model training to avoid initial settling effects.
Figure 3 (not shown) shows stress-SOC curves at different rates. At 0.1C, two inflection points appear near 30% and 60% SOC. As rate increases, the inflection points shift inward and stress values increase, indicating polarization effects at higher currents.
3.2 Data Preprocessing Results
After preprocessing, we constructed datasets with 6 features. For differential stress $\Delta F$, we used a sliding window of $\Delta SOC = 5\%$ to compute monotonicity: $\Delta F = 1$ for increasing, $\Delta F = -1$ for decreasing. This ensures continuity and captures local trends.
3.3 SOC Estimation Results
The trained model was tested on cycles 31–40. Results for charging are shown in Figure 4 (not shown). The estimated SOC closely follows the true SOC except near full charge. The root mean square error (RMSE) for charging is 1.5%, and for discharging is 5.6%. For non-full-cycle tests (SOC 60%–90% for charge, 40%–90% for discharge), accuracy remained similar, confirming robustness.
Table 4 summarizes the performance of different model architectures and input feature sets.
| Model | Input Features | RMSE (%) | MAE (%) |
|---|---|---|---|
| LSTM | 6 features (with stress) | 3.6 | 2.4 |
| BiLSTM | 6 features (with stress) | 2.5 | 2.1 |
| CNN+BiLSTM | 6 features (with stress) | 1.5 | 1.1 |
| LSTM | 3 features (V,I,T) | 6.8 | 5.7 |
| BiLSTM | 3 features (V,I,T) | 6.4 | 5.1 |
| CNN+BiLSTM | 3 features (V,I,T) | 5.4 | 4.5 |
The proposed CNN-BiLSTM with stress features achieves the lowest errors. Compared to models without stress (3 features), the improvement is substantial, especially in the middle SOC plateau where voltage alone is insufficient. The bidirectional temporal modeling of BiLSTM combined with CNN’s local feature extraction effectively captures both the morphological and sequential characteristics of stress and electrical data.
3.4 Comparative Analysis
To further validate the role of stress, we compared the estimation error distribution across SOC ranges. Figure 5 (not shown) indicates that in the mid-SOC region (20%–80%), the error of the 3-feature model increases significantly, while the 6-feature model maintains low error. This confirms that stress provides complementary information that resolves the ambiguity of voltage plateaus in LFP energy storage batteries.
4. Conclusion
In this study, we conducted a comprehensive analysis of stress characteristics of LFP energy storage batteries and developed a CNN-BiLSTM model that fuses electrical and stress parameters for accurate SOC estimation. The voltage plateau issue of LFP batteries is mitigated by incorporating stress data, which exhibits distinct changes in the mid-SOC region. Experimental results show that the proposed method achieves a charging RMSE of 1.5% and significantly outperforms models relying solely on voltage, current, and temperature. The approach is particularly effective for partial SOC windows commonly encountered in practical energy storage operations. This work provides a reliable technique for digital twin applications and enhances the safety and efficiency of energy storage battery systems.