The rapid integration of large-scale renewable energy into power grids presents significant challenges to system stability, creating an ever-growing demand for efficient energy storage solutions. Among various technologies, lithium-ion battery-based energy storage systems have gained paramount importance due to their high efficiency, flexible application, and fast response capabilities. However, the long-term operation of lithium-ion energy storage battery packs under complex and variable grid conditions inevitably leads to issues such as accelerated performance degradation, increased inconsistency among cells, and reduced estimation accuracy for key performance indicators. These problems pose serious threats to the safety, economy, and reliability of energy storage power stations. Therefore, accurately and reliably estimating the State of Health (SOH) of an energy storage battery pack is a critical task. Effective SOH assessment enables the evaluation of remaining useful life and aging degree, which is fundamental for formulating maintenance strategies, optimizing operational control, and ensuring the safe and stable operation of the entire energy storage system.
Traditional methods for battery SOH estimation can be broadly categorized into model-based and data-driven approaches. Model-based methods, such as those using electrochemical models or equivalent circuit models, require precise parameter identification and are often computationally intensive, making them less suitable for online monitoring of complex energy storage battery systems in the field. In recent years, data-driven methods have emerged as powerful alternatives. These methods circumvent the need for complex physical modeling by learning the relationship between easily measurable operational data and battery health degradation directly from historical data. Popular algorithms include Support Vector Regression (SVR), Gaussian Process Regression (GPR), and various neural network architectures, particularly Long Short-Term Memory (LSTM) networks known for handling time-series data.
A crucial step in data-driven SOH estimation is the extraction of informative health indicators or features. Research has extensively explored features from charging voltage curves, incremental capacity (IC) curves, differential temperature curves, and electrochemical impedance. However, many of these features are derived from specific, controlled operating conditions (like constant-current charging segments) or require sophisticated signal processing, which may not be readily available for online monitoring of large-scale energy storage battery packs in real-world applications. Furthermore, most studies focus on the SOH estimation of individual cells. Scaling these methods to an entire energy storage battery pack by estimating the health of each cell individually is computationally prohibitive and impractical for the routine operation and maintenance of energy storage stations containing thousands of cells.
This paper addresses these practical challenges by proposing a novel, early health status detection method for large-capacity lithium iron phosphate (LFP) energy storage battery packs. The core innovation lies in utilizing the voltage range (the difference between the maximum and minimum cell voltage within the pack) as a primary health indicator. This signal is simple to measure, requires no complex transformation, and inherently reflects the consistency and overall aging state of the entire energy storage battery pack. We conduct a full-cycle aging experiment on a commercial 220 Ah LFP battery pack. From the measured voltage range profiles during each cycle, we extract key time-domain features. We then employ correlation analysis to select the most health-relevant features. Finally, we construct an estimation model using a Bidirectional Long Short-Term Memory (BiLSTM) network, whose hyperparameters are optimized by the Sparrow Search Algorithm (SSA). The effectiveness of the proposed voltage range features and the superiority of the SSA-BiLSTM model are validated through comparative studies with conventional machine learning algorithms. The proposed framework offers a practical, efficient, and accurate solution for the online SOH monitoring of large-scale energy storage battery systems.
Methodology
Definition of Key Metrics
For a series-connected energy storage battery pack, its health state can be defined from either capacity or internal resistance perspectives. Given that capacity is a more direct and commonly monitored parameter in field applications, this work adopts the capacity-based definition of SOH:
$$ \text{SOH}_{\text{cap}}(t) = \frac{C_{\text{current}}(t)}{C_{\text{nominal}}} \times 100\% $$
where $C_{\text{current}}(t)$ is the maximum discharge capacity of the pack at cycle $t$, and $C_{\text{nominal}}$ is the rated capacity of the new pack. A SOH of 100% indicates a brand-new pack, and its value decreases as the pack ages.
The State of Charge (SOC) indicates the remaining available energy in the pack and is defined as:
$$ \text{SOC}(t) = \left(1 – \frac{Q_{\text{discharged}}(t)}{C_{\text{current}}(t)}\right) \times 100\% $$
where $Q_{\text{discharged}}(t)$ is the cumulative discharged capacity from a fully charged state.
The central health indicator proposed in this work is the Voltage Range $\Delta U$ of the energy storage battery pack. It is defined as the difference between the maximum and minimum cell voltages within the pack at any given time:
$$ \Delta U(t) = U_{\max}(t) – U_{\min}(t) $$
where $U_{\max}(t)$ and $U_{\min}(t)$ are the maximum and minimum terminal voltages among all series-connected cells in the pack, respectively. This metric is a direct and effective measure of the pack’s inconsistency. As cells age at different rates, their capacities and internal resistances diverge, leading to a more pronounced spread in terminal voltages under load, which is captured by $\Delta U(t)$.
Feature Extraction from Voltage Range Profile
The voltage range $\Delta U(t)$ is not a static value but a dynamic profile that evolves throughout a charge-discharge cycle and, more importantly, across the lifespan of the energy storage battery pack. The objective is to extract salient features from this profile that correlate strongly with the pack’s SOH decay. Based on the characteristic shape of the $\Delta U(t)$ curve, the following five candidate features are initially extracted for each cycle $i$:
| Feature Symbol | Description |
|---|---|
| $U_{s,\text{char}}^{(i)}$ | Voltage range after 30 minutes of relaxation following a charge termination. |
| $U_{s,\text{dis}}^{(i)}$ | Voltage range after 30 minutes of relaxation following a discharge termination. |
| $U_{e,\text{char}}^{(i)}$ | Voltage range at the instant of charge termination (when any cell reaches the upper voltage limit). |
| $U_{e,\text{dis}}^{(i)}$ | Voltage range at the instant of discharge termination (when any cell reaches the lower voltage limit). |
| $T_{\text{range}}^{(i)}$ | The total time duration for the voltage range to complete one full charge-discharge cycle profile. |
Feature Selection via Correlation Analysis
To identify the most health-relevant features from the candidate set, two robust correlation analysis methods are employed: Pearson Correlation Coefficient and Grey Relational Analysis (GRA).
1. Pearson Correlation Coefficient (PCC): This linear correlation metric measures the strength and direction of a linear relationship between a feature sequence $X = \{x^{(1)}, x^{(2)}, …, x^{(N)}\}$ and the SOH sequence $Y = \{\text{SOH}^{(1)}, \text{SOH}^{(2)}, …, \text{SOH}^{(N)}\}$. It is calculated as:
$$ \rho_{XY} = \frac{E(XY) – E(X)E(Y)}{\sqrt{E(X^2) – [E(X)]^2} \cdot \sqrt{E(Y^2) – [E(Y)]^2}} $$
where $E(\cdot)$ denotes the expectation (mean) operator. The value of $\rho_{XY}$ lies in $[-1, 1]$, where values close to 1 or -1 indicate strong linear correlation, and 0 indicates no linear correlation.
2. Grey Relational Analysis (GRA): GRA is a non-linear correlation measure that evaluates the geometric similarity between the shapes of two sequences. It is particularly effective when the relationship is not strictly linear. For a feature sequence $X_i = \{x_i(1), x_i(2), …, x_i(N)\}$ and the SOH reference sequence $Y = \{y(1), y(2), …, y(N)\}$, the grey relational coefficient at step $k$ is:
$$ \xi_i(k) = \frac{\min\limits_{i} \min\limits_{k} |y(k) – x_i(k)| + \rho \cdot \max\limits_{i} \max\limits_{k} |y(k) – x_i(k)|}{|y(k) – x_i(k)| + \rho \cdot \max\limits_{i} \max\limits_{k} |y(k) – x_i(k)|} $$
where $\rho$ is the distinguishing coefficient, typically set to 0.5. The overall Grey Relational Grade (GRG) $r_i$ for feature $i$ is then computed as the average of the coefficients:
$$ r_i = \frac{1}{N} \sum_{k=1}^{N} \xi_i(k) $$
The GRG $r_i$ ranges from 0 to 1, with a higher value indicating a stronger similarity in the developmental trend between the feature and the SOH.
Sparrow Search Algorithm (SSA) Optimized BiLSTM Model
The final SOH estimation model is built upon a Bidirectional Long Short-Term Memory (BiLSTM) network, enhanced by the Sparrow Search Algorithm (SSA) for hyperparameter tuning.
1. BiLSTM Network: Standard LSTM networks process sequential data in a forward direction, capturing dependencies from past states. A BiLSTM network improves upon this by incorporating two separate hidden LSTM layers: one processes the sequence forwards, and the other processes it backwards. This allows the network to capture contextual information from both past and future points for any given timestep within the sequence, leading to a richer representation. The final output $h_t$ at time $t$ is a combination of the forward hidden state $\overrightarrow{h_t}$ and the backward hidden state $\overleftarrow{h_t}$, typically through concatenation or summation:
$$ h_t = \mathcal{F}(\overrightarrow{h_t}, \overleftarrow{h_t}) $$
This architecture is well-suited for learning the temporal degradation patterns present in the sequence of voltage range features.
2. Sparrow Search Algorithm (SSA): Manually tuning BiLSTM hyperparameters (like the number of hidden units, learning rate, and number of training epochs) is time-consuming and suboptimal. SSA is a swarm intelligence optimization algorithm inspired by the foraging and anti-predation behaviors of sparrows. It features fast convergence and strong robustness. The population consists of discoverers, followers, and scouts. The position update rules are as follows:
Discoverer Update:
$$ X_{i,j}^{t+1} = \begin{cases}
X_{i,j}^{t} \cdot \exp\left(-\frac{i}{\alpha \cdot T_{\text{max}}}\right), & \text{if } R_2 < ST \\
X_{i,j}^{t} + Q \cdot L, & \text{if } R_2 \ge ST
\end{cases} $$
Follower Update:
$$ X_{i,j}^{t+1} = \begin{cases}
Q \cdot \exp\left(\frac{X_{\text{worst}}^{t} – X_{i,j}^{t}}{i^2}\right), & \text{if } i > N/2 \\
X_{P}^{t+1} + |X_{i,j}^{t} – X_{P}^{t+1}| \cdot A^{+} \cdot L, & \text{otherwise}
\end{cases} $$
Scout (Alert Sparrow) Update:
$$ X_{i,j}^{t+1} = \begin{cases}
X_{\text{best}}^{t} + \beta \cdot |X_{i,j}^{t} – X_{\text{best}}^{t}|, & \text{if } f_i > f_g \\
X_{i,j}^{t} + K \cdot \left( \frac{|X_{i,j}^{t} – X_{\text{worst}}^{t}|}{(f_i – f_w) + \epsilon} \right), & \text{if } f_i = f_g
\end{cases} $$
where $X_{i,j}$ represents the position of the $i$-th sparrow in the $j$-th dimension, $t$ is the current iteration, $T_{\text{max}}$ is the maximum iterations, $\alpha$, $R_2$, $ST$, $Q$, $L$, $A^{+}$, $\beta$, $K$ are algorithm parameters, $f_i$, $f_g$, $f_w$ are fitness values, and $\epsilon$ is a small constant. SSA is used to find the optimal set of hyperparameters that minimize the prediction error (e.g., Root Mean Square Error) of the BiLSTM model on a validation set.
Overall Framework
The complete workflow for the early health status detection of the energy storage battery pack is as follows:
- Data Acquisition: Perform cyclic aging tests on the target energy storage battery pack, recording voltage, current, temperature, and calculating capacity and voltage range $\Delta U(t)$ for each cycle.
- Feature Extraction & Selection: Extract the five candidate voltage range features from each cycle’s $\Delta U(t)$ profile. Apply PCC and GRA to select the subset of features with the strongest correlation to SOH decay.
- Model Building & Optimization: Construct a BiLSTM network. Use the SSA to optimize its key hyperparameters by searching for the configuration that yields the lowest prediction error.
- Training & Evaluation: Train the optimized SSA-BiLSTM model using historical data (feature sequences as input, SOH as output). Evaluate its performance on unseen test data using standard metrics.
- Online Monitoring: Deploy the trained model to estimate the real-time SOH of the energy storage battery pack based on incoming voltage range measurements.
Experimental Setup and Data Acquisition
To validate the proposed method, a cyclic aging experiment was conducted on a large-capacity lithium iron phosphate energy storage battery pack. The test subject was a commercial BYD module, model MCRSA08-LC, comprising eight 220 Ah prismatic LFP cells connected in series.
| Parameter | Specification |
|---|---|
| Nominal Voltage | 25.6 V |
| Nominal Capacity | 220 Ah (±10%) |
| Cell Charge Cut-off Voltage | 3.65 V |
| Cell Discharge Cut-off Voltage | 2.7 V |
The testing platform consisted of a Ningbo Bate BT60V300AC2 battery test system (0-60V, 300A max), a HCJB1000L-20 temperature chamber set to a constant 25°C, and a host computer for test control and data monitoring.
The cyclic aging protocol was designed to simulate a full depth-of-discharge cycle typical of energy storage battery applications:
- Charge: Constant Current (CC) charge at 0.5C (approximately 110 A) until any single cell voltage reaches 3.65 V.
- Rest: Relax for 30 minutes.
- Discharge: Constant Current (CC) discharge at 0.5C until any single cell voltage drops to 2.7 V.
- Rest: Relax for 30 minutes. The total discharged capacity in this step is recorded as the maximum available capacity for that cycle.
This sequence constitutes one full cycle. The energy storage battery pack underwent 720 such cycles. The initial maximum capacity was measured at 240 Ah. After 720 cycles, the capacity had faded to 218 Ah, representing a clear aging trend. Throughout the experiment, cell voltages, pack current, and temperature were sampled at a high frequency, enabling the calculation of the voltage range $\Delta U(t)$ and SOH for every cycle.
Results Analysis and Discussion
Voltage Range Behavior and Feature Correlation
The voltage range $\Delta U(t)$ profiles exhibited characteristic patterns that evolved with cycling. Key observations include: 1) A sharp rise in $\Delta U(t)$ near the end of discharge (low SOC) due to the divergent terminal voltages of inconsistent cells as they approach the lower cutoff limit. 2) A noticeable rise in $\Delta U(t)$ near the end of charge (high SOC) for similar reasons. 3) A gradual relaxation and stabilization of $\Delta U(t)$ during the 30-minute rest periods after charge and discharge. Critically, the stabilized voltage range values after the discharge rest period ($U_{s,\text{dis}}$) showed a clear, monotonic decreasing trend as the number of cycles increased, visually correlating with the capacity fade trend. This aligns with the theory that as the weakest cell in the energy storage battery pack ages more rapidly, its polarization characteristics change more significantly, affecting the steady-state voltage difference after relaxation.
The quantitative correlation analysis results for all five candidate features are summarized below. We set thresholds of |PCC| > 0.8 and GRG > 0.7 to select highly relevant health factors.
| Feature | Pearson Correlation Coefficient (PCC) | Grey Relational Grade (GRG) | Selected? |
|---|---|---|---|
| $U_{s,\text{char}}$ | 0.9795 | 0.7428 | Yes |
| $U_{s,\text{dis}}$ | 0.9835 | 0.9594 | Yes |
| $U_{e,\text{char}}$ | -0.7451 | 0.5706 | No |
| $U_{e,\text{dis}}$ | -0.8026 | 0.6775 | No |
| $T_{\text{range}}$ | 0.9415 | 0.6839 | No |
The features $U_{s,\text{char}}$ and $U_{s,\text{dis}}$, representing the voltage range after charge and discharge relaxation, respectively, demonstrated exceptionally high correlation with SOH. They were therefore selected as the final health factor vector $HF^{(i)} = [U_{s,\text{char}}^{(i)}, U_{s,\text{dis}}^{(i)}]$ for input into the estimation models.
Model Construction and Optimization
The dataset of 720 cycles was split into a training set (first 500 cycles) and a test set (last 220 cycles). The SSA was configured with a population size of 15 and a maximum of 20 iterations to optimize three key hyperparameters of the BiLSTM model: the number of hidden units, the initial learning rate, and the maximum number of training epochs. The objective function for SSA was to minimize the Root Mean Square Error (RMSE) on a held-out validation set. The SSA converged efficiently, finding an optimal configuration with 119 hidden units, an initial learning rate of 0.0191, and 148 training epochs.
Model Performance and Validation
The performance of the proposed SSA-BiLSTM model was compared against three established data-driven models: Gaussian Process Regression (GPR) with a Radial Basis Function (RBF) kernel, Support Vector Regression (SVR) with an RBF kernel, and a standard LSTM network. All models were trained and tested on the same dataset using the selected health factors ($U_{s,\text{char}}$, $U_{s,\text{dis}}$).
The estimation results and the corresponding absolute errors are shown conceptually in the results. Quantitatively, the prediction accuracy was evaluated using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE):
$$ \text{RMSE} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (\text{SOH}_{\text{true}}^{(i)} – \text{SOH}_{\text{est}}^{(i)})^2} $$
$$ \text{MAE} = \frac{1}{N} \sum_{i=1}^{N} |\text{SOH}_{\text{true}}^{(i)} – \text{SOH}_{\text{est}}^{(i)}| $$
The performance metrics for all models are summarized below:
| Model | Root Mean Square Error (RMSE) | Mean Absolute Error (MAE) |
|---|---|---|
| SSA-BiLSTM (Proposed) | 7.108 × 10-4 | 6.08 × 10-4 |
| Gaussian Process Regression (GPR) | 4.726 × 10-3 | 3.77 × 10-3 |
| Long Short-Term Memory (LSTM) | 1.749 × 10-3 | 1.60 × 10-3 |
| Support Vector Regression (SVR) | 1.886 × 10-3 | 1.76 × 10-3 |
Discussion of Results:
- Effectiveness of Voltage Range Features: A critical finding is that under all tested models, the SOH estimation absolute error remained within ±0.8%. This conclusively demonstrates that the simple, easy-to-measure voltage range features $U_{s,\text{char}}$ and $U_{s,\text{dis}}$ are highly effective health indicators for the energy storage battery pack. They successfully encode the pack’s aging trend without requiring individual cell analysis, significantly reducing the complexity of pack-level SOH monitoring.
- Superiority of the SSA-BiLSTM Model: The proposed SSA-BiLSTM model achieved the lowest prediction errors, with an RMSE of only 0.07% and an MAE of 0.061%. This represents a substantial improvement over the conventional models.
- GPR, while principled, showed higher error, possibly due to sensitivity to kernel and hyperparameter choices which were not as rigorously optimized.
- SVR exhibited moderate performance but is generally less robust to outliers and may struggle with complex, non-linear temporal dependencies.
- The standard LSTM performed better than GPR and SVR but was outperformed by its bidirectional counterpart. This validates the advantage of BiLSTM in capturing more comprehensive contextual information from the time-series health factor data.
- The use of SSA for hyperparameter tuning was crucial. It automated the search for an optimal model configuration, avoiding suboptimal manual tuning and ensuring the BiLSTM network reached its full potential for this specific task of energy storage battery pack SOH estimation.
The results confirm that the synergy of informative voltage-based health factors, a powerful bidirectional recurrent neural network, and an intelligent optimization algorithm creates a robust and accurate framework for online SOH estimation. This method is directly applicable to the condition monitoring of large-scale energy storage battery systems in the field.
Conclusion
This paper presented a novel, practical framework for the early detection of health status in large-capacity lithium iron phosphate energy storage battery packs. The core contribution is the identification and utilization of voltage range characteristics, specifically the steady-state voltage difference after charge and discharge relaxation periods, as highly effective health indicators. These features are directly measurable from the energy storage battery pack’s management system without the need for complex transformations or individual cell analysis, offering a significant practical advantage.
Through rigorous cyclic aging tests and correlation analysis, the selected features were proven to strongly correlate with pack capacity fade. Furthermore, a sophisticated estimation model was developed by integrating a Bidirectional Long Short-Term Memory (BiLSTM) network with the Sparrow Search Algorithm (SSA) for hyperparameter optimization. The proposed SSA-BiLSTM model demonstrated superior estimation accuracy compared to conventional machine learning models like GPR, SVR, and standard LSTM, achieving an exceptionally low RMSE of 0.07%.
The proposed method effectively addresses the challenge of pack-level SOH estimation by focusing on pack-level measurements that encapsulate the collective aging behavior. It provides a feasible, accurate, and efficient solution for the online health monitoring of energy storage battery systems, which is vital for predictive maintenance, lifespan management, and ensuring the safe and reliable operation of grid-scale energy storage facilities. Future work will focus on validating the model’s generalizability under more realistic, dynamic grid service profiles (e.g., frequency regulation, peak shaving) and exploring its adaptability to different chemistries and configurations of energy storage battery packs.