In the context of global energy transition and sustainable development, optimizing energy structures and advancing smart grid technologies have become pivotal drivers of societal progress. Energy storage systems, as critical components for balancing grid supply and demand while enhancing energy utilization efficiency, are increasingly vital. Among various energy storage solutions, lithium iron phosphate (LiFePO4) energy storage cells stand out due to their excellent safety profile and long cycle life, making them widely adopted in applications such as smart grids, residential energy storage, and electric vehicles. However, as deployment scenarios grow more complex, safety concerns persist, particularly regarding stress variations induced by structural constraints in battery modules. These stress changes during charging and discharging can lead to structural deformations and even safety incidents. Therefore, investigating the stress characteristics of LiFePO4 energy storage cells, exploring the relationship between stress dynamics and cell states, and developing state estimation algorithms that integrate stress and electrical parameters are essential for improving digital twin capabilities and safety management in energy storage systems.
LiFePO4 energy storage cells exhibit broad voltage plateaus in both positive and negative electrodes, which complicates accurate state of charge (SOC) estimation using voltage sensors alone, especially within the plateau regions (e.g., 40%–90% SOC). Moreover, the relatively stable operating currents in energy storage systems hinder parameter observability in battery models. Since SOC cannot be directly measured, it must be inferred from physical parameters like current, voltage, temperature, and stress. Traditional SOC estimation methods include ampere-hour integration, open-circuit voltage (OCV) correlation, model-based filtering, and machine learning approaches. Ampere-hour integration relies on current integration over time but suffers from error accumulation without periodic calibration. OCV methods leverage the voltage-SOC relationship; however, the flat OCV-SOC curve of LiFePO4 cells reduces reliability in plateau regions. Model-based methods, such as Kalman filters (e.g., extended or unscented variants), incorporate battery models but face challenges in nonlinear system handling. Data-driven approaches, including machine and deep learning, have gained traction by modeling complex mappings from operational data to SOC.
Recent studies highlight the role of stress characteristics in optimizing and assessing energy storage cell performance. Applying appropriate compressive force can enhance electrode-electrolyte contact, improving cell efficiency. In module assembly, typical preload forces range from tens to hundreds of kilograms. Stress variations correlate with SOC changes, providing an additional dimension for state estimation. Given the limitations of single-parameter methods, multi-parameter fusion techniques leveraging electrical, thermal, and mechanical data have emerged as promising solutions. Digital twin platforms enable real-time multi-source data acquisition, facilitating advanced state estimation through virtual-physical interactions. This study focuses on analyzing stress characteristics in LiFePO4 energy storage cells and developing a deep learning-based SOC estimation model that combines stress and electrical parameters. Experiments under varying rates and preload conditions reveal stress dynamics, and a convolutional neural network-bidirectional long short-term memory (CNN-BiLSTM) model is designed to capture data morphology and temporal evolution. Results demonstrate that integrating stress characteristics with machine learning enhances SOC estimation accuracy, offering a novel approach for digital twin and safety management of LiFePO4 energy storage cells.
Methodology
To analyze the stress characteristics of LiFePO4 energy storage cells, experiments were conducted under controlled conditions. The cells used were commercial LiFePO4 samples with a nominal capacity of 25 Ah, nominal voltage of 3.2 V, and dimensions of 238.0 mm × 140.0 mm × 7.6 mm. The maximum charge and discharge rates were 1 C and 2 C, respectively, with charge and discharge cutoff voltages of 3.65 V and 2.5 V. The experimental setup comprised three steel plates, with the energy storage cell placed between two plates. A preload force was applied using a spoke-type pressure sensor, and nuts were tightened at the corners to achieve specific preload levels (e.g., 500 kg). Stress and temperature data were recorded at 10 s intervals using a multi-channel data acquisition system (Rigol M300), while voltage and current data were logged by a charge-discharge cycler.
The experimental procedure involved initial characterization tests to extract capacity and stress-electrical features, followed by cyclic charge-discharge tests to generate datasets for model training and validation. Specifically, energy storage cells were charged at 1 C constant current to 3.65 V, rested for 1 h, discharged at 1.5 C to 2.5 V, and rested again for 1 h. This cycle was repeated 40 times to collect comprehensive data. Key parameters monitored included charge variation (ΔQ), stress variation (ΔF), voltage (V), current (I), stress (F), and temperature (T). Data preprocessing involved time alignment, segmentation of charge-discharge segments, and removal of rest periods. Differential parameters (ΔQ and ΔF) were computed to emphasize dynamic changes, and data were smoothed using moving average filters to reduce noise. The 3-Sigmoid rule was applied to eliminate outliers, ensuring a clean dataset for analysis.
The stress characteristics of energy storage cells were analyzed by examining electrode thickness changes and external stress under mechanical constraints. During charging, the LiFePO4 cathode volume decreases linearly by up to 7%, while the graphite anode exhibits non-monotonic thickness increases of up to 8%. The combined effect results in non-monotonic stress variations, with overall increasing trends during charging and decreasing trends during discharging. The relationship between electrode thickness, stress, and SOC can be expressed as follows. Let $$S_{\text{stress}}$$ represent the stress, and $$SOC$$ denote the state of charge. The stress evolution is modeled as: $$S_{\text{stress}} = f(SOC, I, T) + \epsilon$$ where $$f$$ is a nonlinear function, and $$\epsilon$$ accounts for noise. Experimental data under different rates (0.1 C to 1 C) showed that stress curves exhibit inflection points at specific SOC values (e.g., 30% and 60% at low rates), which shift or diminish at higher rates due to polarization effects.
For SOC estimation, a CNN-BiLSTM model was developed to leverage multi-parameter inputs. The model integrates 1D convolutional neural networks (CNN) for local feature extraction and bidirectional long short-term memory (BiLSTM) networks for temporal dependency capture. The input features include ΔQ, ΔF, V, I, F, and T. The CNN layer employs 3×1 convolution kernels with 64 output channels, ReLU activation, and pooling to retain key morphological features (e.g., voltage plateau拐点 and stress slopes). The BiLSTM component consists of two bidirectional LSTM layers, each with 128 memory units, processing sequences in forward and backward directions to learn historical and future dependencies. The final output is a 256-dimensional feature vector passed through a fully connected layer with dropout (30%) for SOC regression.
The LSTM gate mechanisms are defined as follows. The forget gate $$f_t$$, input gate $$i_t$$, and output gate $$o_t$$ are computed as: $$f_t = \sigma(W_f [h_{t-1}, x_t] + b_f)$$ $$i_t = \sigma(W_i [h_{t-1}, x_t] + b_i)$$ $$o_t = \sigma(W_o [h_{t-1}, x_t] + b_o)$$ where $$W_f$$, $$W_i$$, and $$W_o$$ are weight matrices; $$b_f$$, $$b_i$$, and $$b_o$$ are bias vectors; $$h_{t-1}$$ is the previous hidden state; $$x_t$$ is the current input; and $$\sigma$$ is the sigmoid function. The cell state $$C_t$$ and hidden state $$h_t$$ are updated as: $$\tilde{C}_t = \tanh(W_c [h_{t-1}, x_t] + b_c)$$ $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t$$ $$h_t = o_t \odot \tanh(C_t)$$ where $$\odot$$ denotes element-wise multiplication. The BiLSTM concatenates forward and backward outputs to form the final hidden state.
Data normalization was performed using min-max scaling to [0,1]. The model was trained with mean squared error (MSE) loss, Adam optimizer (learning rate 0.001, momentum 0.9), gradient clipping (threshold 5.0), and batch size 64 over 200 epochs. Datasets from cycles 10–30 were used for training (60%), validation (20%), and testing (20%). To evaluate generalization, partial SOC segments (e.g., 60%–90% for charging, 40%–90% for discharging) were tested alongside full cycles.
Results and Analysis
The stress characteristics of LiFePO4 energy storage cells were evaluated under various operational conditions. Figure 4 illustrates the voltage and stress profiles during a typical charge-discharge cycle. The voltage remains relatively flat in the mid-SOC range (40%–90%), while stress shows non-monotonic variations, with an initial preload of approximately 495 kg and peaks up to 530 kg. The stress change of about 35 kg provides a distinguishable feature for SOC estimation, especially in plateau regions where voltage-based methods struggle. Over 40 cycles, stress consistency improved after the initial cycles, indicating stabilization between the energy storage cell and fixture. Long-term aging effects, such as irreversible thickness increases, were observed but not addressed in this study.
Table 1 summarizes the key parameters of the energy storage cells used in experiments.
| Parameter | Value |
|---|---|
| Nominal Capacity | 25 Ah |
| Nominal Voltage | 3.2 V |
| Dimensions | 238.0 mm × 140.0 mm × 7.6 mm |
| Max Charge Rate | 1 C |
| Max Discharge Rate | 2 C |
| Charge Cutoff Voltage | 3.65 V |
| Discharge Cutoff Voltage | 2.5 V |
Stress behavior under different current rates is depicted in Figure 6. At 0.1 C, stress curves show inflection points near SOC = 30% and SOC = 60%. As the rate increases to 1 C, these inflection points diminish due to polarization, and stress magnitudes rise. This highlights the sensitivity of stress to operational conditions, reinforcing its utility in multi-parameter fusion for energy storage cell state estimation.
The CNN-BiLSTM model’s performance was assessed using cycles 30–40 for testing. For charging, the SOC estimation achieved a root mean square error (RMSE) of 1.5%, while discharging RMSE was 5.6%. Figure 7 presents the SOC estimation results, showing close alignment with reference values except near SOC extremes. In non-full cycles (e.g., 60%–90% SOC segments), the model maintained reliability, with errors comparable to full-cycle tests. Comparative analysis with a baseline method using only voltage, current, and temperature (3 parameters) revealed higher errors in mid-SOC regions (RMSE up to 6.8%), underscoring the value of stress integration. The differential stress parameter (ΔF) proved particularly effective in capturing dynamic changes during plateaus.
Table 2 compares the CNN-BiLSTM model with alternative architectures using 6-parameter inputs (including stress) and 3-parameter inputs (without stress).
| Model | Input Parameters | RMSE (%) | MAE (%) |
|---|---|---|---|
| LSTM | 6 (with stress) | 3.6 | 2.4 |
| BiLSTM | 6 (with stress) | 2.5 | 2.1 |
| CNN-BiLSTM | 6 (with stress) | 1.5 | 1.1 |
| LSTM | 3 (without stress) | 6.8 | 5.7 |
| BiLSTM | 3 (without stress) | 6.4 | 5.1 |
| CNN-BiLSTM | 3 (without stress) | 5.4 | 4.5 |
The CNN-BiLSTM model with stress parameters reduced RMSE by 58.3% compared to LSTM and 41.7% compared to BiLSTM alone. This demonstrates the synergistic effect of CNN’s feature extraction and BiLSTM’s temporal modeling in enhancing SOC estimation for energy storage cells. The integration of stress parameters mitigates uncertainties in voltage plateaus, providing a more robust solution for practical energy storage applications.
Discussion
The integration of stress characteristics with electrical parameters addresses key limitations in LiFePO4 energy storage cell state estimation. The non-monotonic stress variations during charging and discharging offer complementary information to voltage, especially in plateau regions where voltage-based methods exhibit high uncertainty. The CNN-BiLSTM model effectively leverages this multi-dimensional data through convolutional layers that extract local features (e.g., stress slope changes) and bidirectional recurrent layers that capture long-term dependencies. This approach is particularly suited for energy storage systems operating under steady currents, where model parameter identifiability is challenging.
The stress response in energy storage cells is influenced by factors such as preload force, current rate, and cycle number. At lower rates, stress inflection points provide distinct SOC markers, but polarization at higher rates smooths these features. Nevertheless, the overall stress-SOC mapping remains valuable when combined with other parameters. Data preprocessing, including differential parameter computation and smoothing, enhances feature discriminability. The model’s performance in partial SOC segments confirms its applicability to real-world scenarios where energy storage cells rarely undergo full cycles.
Comparative results highlight the importance of stress data. Without stress, estimation errors increase significantly in mid-SOC ranges due to voltage flatness. The CNN-BiLSTM architecture outperforms simpler models by simultaneously addressing spatial and temporal complexities. Future work could explore adaptive learning for aging energy storage cells and real-time deployment on digital twin platforms. Overall, the fusion of stress and electrical parameters via deep learning offers a promising path toward accurate and reliable state estimation for LiFePO4 energy storage cells.
Conclusion
This study investigated the stress characteristics of lithium iron phosphate energy storage cells and developed a SOC estimation method based on electro-mechanical parameter fusion and a CNN-BiLSTM model. Experiments under varying rates and preload conditions revealed non-monotonic stress dynamics that correlate with SOC, providing an additional dimension for state inference. The proposed model combines CNN for local feature extraction and BiLSTM for temporal sequence modeling, achieving an RMSE of 1.5% for charging SOC estimation. The inclusion of stress parameters significantly improved accuracy in voltage plateau regions compared to conventional electrical-only methods. This approach can be deployed on digital twin platforms for energy storage systems, enhancing SOC estimation robustness and supporting safety management. Future research will focus on extending the method to aging energy storage cells and optimizing computational efficiency for real-time applications.