The safe and efficient operation of modern grid-scale Battery Energy Storage Systems (BESS) is fundamentally dependent on accurate knowledge of the State of Charge (SOC) for every individual energy storage cell within a cluster. SOC, defined as the ratio of remaining usable charge to the current maximum available capacity, is a critical parameter for preventing over-charge and over-discharge events, managing cell balancing, and optimizing system performance and lifespan. It is formally expressed as:
$$SOC = \frac{Q_{\text{remain}}}{Q_{\text{rated}}} \times 100\%$$
where \(Q_{\text{remain}}\) is the remaining charge capacity and \(Q_{\text{rated}}\) is the nominal rated capacity of the energy storage cell. Direct measurement of SOC via sensors is impractical in online operation. Consequently, accurate estimation algorithms are indispensable for battery management systems (BMS). While significant research has advanced SOC estimation for single cells, the problem is markedly more complex for an energy storage cell cluster, where hundreds of cells are connected in series and/or parallel. Manufacturing tolerances, material inconsistencies, and varying operational histories lead to inherent cell-to-cell variations in parameters like capacity, internal resistance, and aging rates. Treating a cluster as a homogeneous entity or simply replicating a single-cell estimator fails to capture these disparities and the collective behavior of the cluster, leading to potentially unsafe and inaccurate estimates for individual energy storage cells.
This work addresses the critical challenge of fine-grained, multi-cell SOC estimation within an energy storage cell cluster. We propose a novel deep learning architecture named the Cell Memory and Cluster Feature fusion network (CMCF). The CMCF network is designed to intelligently integrate information from multiple perspectives: the detailed temporal data from each individual energy storage cell, holistic statistical features representing the global state of the entire cluster, and a memory mechanism that learns and recalls typical operational patterns and cell-specific characteristics. This fusion enables a robust and precise estimation of SOC for every cell in the cluster, accounting for both individual disparities and collective dynamics.
The primary contributions of this method are twofold. First, it introduces a dual-perspective input scheme that explicitly models both cell-level and cluster-level information. Expert-engineered cluster features provide the model with a global context of the energy storage cell cluster’s operating condition, which serves as crucial auxiliary information for individual cell estimation. Second, it incorporates a trainable memory module that learns to encapsulate prototypical features and inherent differences among energy storage cells. This allows the model to perform a more nuanced characterization of each cell beyond its immediate sensory data. By fusing cell features, cluster features, and memory-retrieved features through an attention-based mechanism, the CMCF network achieves superior estimation accuracy for all energy storage cells within a cluster, as validated on real-world operational data from a lithium iron phosphate (LFP) battery energy storage system.
Existing SOC Estimation Paradigms: A Review
The quest for accurate SOC estimation has led to the development of various methodologies, which can be broadly categorized into three groups: direct measurement/coulomb counting, model-based filtering approaches, and data-driven techniques. Each paradigm has its strengths and limitations, particularly when scaled to the multi-cell context of an energy storage cell cluster.
1. Coulomb Counting (Ampere-hour Integration): This is the most straightforward method, which calculates SOC by integrating the current flowing into or out of the battery over time.
$$SOC(t) = SOC(t_0) + \frac{1}{Q_{\text{rated}}} \int_{t_0}^{t} \eta I(\tau) d\tau$$
where \(SOC(t_0)\) is the initial SOC, \(I\) is the current (positive for discharge), and \(\eta\) is the coulombic efficiency. While simple, its major drawback is the open-loop nature. Errors in the initial SOC, current sensor inaccuracies, and unknown capacity fade (\(Q_{\text{rated}}\) changes over time) accumulate without correction, making it unreliable for long-term operation of any energy storage cell.
2. Model-Based Methods: These methods rely on a mathematical model that establishes a relationship between measurable signals (terminal voltage, current) and the internal state (SOC). They typically employ filtering algorithms to optimally estimate the state from noisy measurements.
- Electrochemical Models (EM): These are first-principle models based on porous electrode theory and concentrated solution theory, described by coupled partial differential equations. They offer deep physical insight but are computationally prohibitive for real-time BMS applications in large energy storage cell clusters.
- Equivalent Circuit Models (ECM): These models use electrical components (voltage sources, resistors, capacitors) to approximate the dynamic behavior of an energy storage cell. Common models include the Rint, Thevenin, and dual-polarization (DP) models. The model parameters (e.g., Ohmic resistance, polarization resistance/capacitance) are often SOC and temperature dependent. Algorithms like the Kalman Filter (KF), Extended KF (EKF), and Unscented KF (UKF) are then used to jointly estimate the SOC and sometimes the model parameters. While effective for single cells, their performance in a cluster degrades due to the need for accurate parameterization of each cell’s unique model, increasing complexity and computational load significantly.
3. Data-Driven Methods: With the advent of powerful machine learning and abundant operational data, data-driven approaches have gained prominence. These methods bypass explicit physical modeling and learn the direct mapping from measurable input sequences (voltage, current, temperature) to the target SOC. They are particularly suitable for capturing complex, non-linear battery dynamics.
- Traditional Machine Learning: Methods like Support Vector Regression (SVR) have been applied to SOC estimation.
- Deep Learning: Deep neural networks, with their superior capacity for learning temporal dependencies and complex patterns, have shown remarkable success. Popular architectures include:
- Multi-Layer Perceptrons (MLP) for learning static non-linear mappings.
- Recurrent Neural Networks (RNN), especially Long Short-Term Memory (LSTM) networks and Gated Recurrent Units (GRU), which are adept at handling time-series data.
- Temporal Convolutional Networks (TCN), which use causal convolutions to capture long-range dependencies efficiently.
- Hybrid models (e.g., CNN-LSTM, TCN-LSTM) that combine feature extraction and temporal modeling.
A critical gap in most existing data-driven research is the focus on a single energy storage cell. When applied to a cluster, a naive approach is to train one independent estimator per cell, which is resource-intensive and ignores the valuable inter-cell correlations and global cluster state. Alternatively, training one universal estimator on pooled cell data fails to learn and adapt to the persistent differences between individual energy storage cells. The CMCF network proposed here is designed specifically to close this gap by adopting a holistic, cluster-aware, yet cell-specific estimation strategy. The table below summarizes the key characteristics of these paradigms.
| Paradigm | Key Principle | Advantages | Disadvantages for Cell Clusters |
|---|---|---|---|
| Coulomb Counting | Current time integration. | Simple, low computational cost. | Error accumulation, requires perfect initial SOC, ignores cell variations. |
| Model-Based (ECM+EKF) | Physics-inspired model with state filtering. | Provides uncertainty bounds, can be accurate with good model. | Complex parameter identification per cell, computationally heavy for many cells, model inaccuracy affects performance. |
| Data-Driven (e.g., LSTM) | Learning input-output mapping from data. | No need for explicit model, can capture complex non-linearities. | Typically designed for single cells; ignores cluster context and inter-cell relationships when applied naively. |
| Proposed CMCF | Dual-perspective deep learning with memory. | Explicitly models cell & cluster info, learns cell-specific patterns, suitable for multi-cell estimation. | Requires substantial training data from the cluster, more complex architecture. |
The CMCF Network Architecture
The core objective of the CMCF network is to estimate the SOC for each of the \(N\) energy storage cells in a cluster simultaneously, leveraging both their individual temporal data and the collective knowledge of the cluster’s state. Let the input for the \(i\)-th cell be its historical sequence of measurements (e.g., voltage, temperature), denoted as \(\mathbf{x}_i^c \in \mathbb{R}^{J \times T}\), where \(J\) is the number of measured variables per cell and \(T\) is the sequence length. The shared measurement for the series-connected cluster (e.g., current) is \(\mathbf{f}_J\). The target output is the SOC value \(y_i\) for each cell at the current time step. The overall architecture is illustrated in the following figure and consists of five main components: the Shared Cell Encoder, the Cluster Encoder, the Memory Module, the Feature Fusion block, and the SOC Estimator.
1. Input Feature Engineering: Cell and Cluster Perspectives
The model ingests information from two distinct but complementary perspectives: the Cell View and the Cluster View.
Cell Features: Each energy storage cell’s raw temporal data \(\mathbf{x}_i^c\) is flattened into a 1D vector and processed through a Shared Cell Encoder \(E_c\). This encoder is composed of a stack of Residual MLP (ResMLP) blocks, which help mitigate issues like vanishing gradients when processing sequential data with potential redundancies. The encoder transforms the input into a high-level latent representation \(\mathbf{z}_i^c \in \mathbb{R}^D\) for each cell:
$$\mathbf{z}_i^c = E_c(\text{flatten}(\mathbf{x}_i^c)), \quad i=1,2,…,N$$
The parameters of \(E_c\) are shared across all cells, allowing the model to learn a common feature extraction basis while the subsequent modules handle cell-specificity.
Cluster Features: To provide global context, we construct a set of expert-engineered Cluster Features \(\mathbf{x}^g \in \mathbb{R}^{G \times T}\). These features are statistical summaries computed from the measurements of all \(N\) energy storage cells in the cluster at each time step, capturing the overall operating condition and the degree of inconsistency within the cluster. For a measured variable \(\mathbf{v}\) (e.g., cell voltage) represented as \(\mathbf{v}_i\) for the \(i\)-th cell, we compute features like mean, variance, skewness, kurtosis, and peak-to-peak value across the cluster. For a series-connected cluster, the shared current is also included as-is. The cluster feature vector is then flattened and encoded by a dedicated Cluster Encoder \(E_g\), which has a similar ResMLP structure, to produce a global cluster context feature \(\mathbf{z}^g \in \mathbb{R}^D\):
$$\mathbf{z}^g = E_g(\text{flatten}(\mathbf{x}^g))$$
This \(\mathbf{z}^g\) is replicated and associated with every energy storage cell in the subsequent fusion step, providing each cell’s estimator with the same global “situation awareness”.
2. Memory Module for Prototypical Cell Pattern Learning
To explicitly capture and recall the typical operational patterns and inherent characteristics that differentiate one energy storage cell from another within the cluster, we incorporate a trainable Memory Module. This module contains \(M\) memory items (prototypes) \(\{\mathbf{p}_1, \mathbf{p}_2, …, \mathbf{p}_M\}\), where each \(\mathbf{p}_m \in \mathbb{R}^D\), initialized randomly. During operation, the encoded cell feature \(\mathbf{z}_i^c\) acts as a query.
The module performs a Read operation: it computes the cosine similarity between the query \(\mathbf{z}_i^c\) and all memory items \(\mathbf{p}_m\), generating an attention weight \(w_{i,m}\) via softmax. A weighted sum of the memory items based on these weights produces a memory feature \(\mathbf{z}_i^m\) for the cell:
$$w_{i,m} = \frac{\exp(\mathbf{p}_m^T \mathbf{z}_i^c)}{\sum_{m’=1}^{M} \exp(\mathbf{p}_{m’}^T \mathbf{z}_i^c)}$$
$$\mathbf{z}_i^m = \sum_{m=1}^{M} w_{i,m} \mathbf{p}_m$$
This \(\mathbf{z}_i^m\) effectively retrieves a combination of stored prototypical patterns most relevant to the current state of the \(i\)-th energy storage cell.
During training, an Update operation is also performed to progressively refine the memory items using the incoming queries, ensuring they learn meaningful and discriminative prototypes that represent the various modes and disparities present in the energy storage cell cluster.
3. Cluster-Attention Based Feature Fusion
At this stage, for the \(i\)-th energy storage cell, we have three distinct feature vectors: the original cell feature \(\mathbf{z}_i^c\), the cluster context feature \(\mathbf{z}^g\), and the memory-retrieved feature \(\mathbf{z}_i^m\). Simply concatenating them may not optimally leverage their relationships. Inspired by the self-attention mechanism, we design a Cluster-Attention module for fusion. Here, the cluster feature \(\mathbf{z}^g\) is projected to form the Query (\(\mathbf{Q}\)), the memory feature \(\mathbf{z}_i^m\) is projected to form the Key (\(\mathbf{K}_i\)), and the cell feature \(\mathbf{z}_i^c\) is projected to form the Value (\(\mathbf{V}_i\)). The attention mechanism allows the model to dynamically decide which aspects of the global cluster context (Query) are most relevant based on the cell’s current prototypical pattern (Key), and then use this to selectively refine the core cell feature (Value).
$$\mathbf{A}_i = \text{softmax}\left(\frac{\mathbf{Q} \mathbf{K}_i^T}{\sqrt{d_k}}\right)$$
$$\mathbf{z}_i = \mathbf{A}_i \mathbf{V}_i$$
where \(\mathbf{z}_i \in \mathbb{R}^{d_k}\) is the final fused feature for the \(i\)-th energy storage cell. This design prioritizes the cell’s own data (\(\mathbf{V}_i\)) as the primary carrier of information, while using the memory-influenced attention to gate relevant global cluster insights.
4. SOC Estimation and Training
The fused feature \(\mathbf{z}_i\) for each energy storage cell is passed through a lightweight SOC Estimator, typically a small MLP, to generate the final SOC estimate \(\hat{y}_i\). The entire CMCF network is trained end-to-end using a combined loss function \(\mathcal{L}\):
$$\mathcal{L} = \lambda_1 \mathcal{L}_{\text{mse}} + \lambda_2 \mathcal{L}_{\text{compact}} + \lambda_3 \mathcal{L}_{\text{separate}}$$
where \(\mathcal{L}_{\text{mse}} = \frac{1}{N} \sum_{i=1}^{N}(y_i – \hat{y}_i)^2\) is the mean squared error for SOC estimation. \(\mathcal{L}_{\text{compact}}\) and \(\mathcal{L}_{\text{separate}}\) are auxiliary losses applied to the memory module, encouraging queries to be close to their nearest memory item and memory items to be sufficiently diverse, respectively. The hyperparameters \(\lambda_1, \lambda_2, \lambda_3\) balance these objectives.
Experimental Validation on Real-World Energy Storage Data
The performance of the proposed CMCF network was rigorously evaluated using operational data from a real-world grid-scale Lithium Iron Phosphate (LFP) energy storage system. The test involved a single battery cluster comprising 224 energy storage cells connected in series. Each cell provided voltage and surface temperature measurements, while the cluster current was shared. Multiple complete charge cycles were used, with several cycles for training and a held-out cycle for testing. Data was normalized before training.
Evaluation Metrics and Compared Methods
To comprehensively assess performance, we employed four key metrics calculated over all cells and timesteps in the test set:
- Mean Squared Error (MSE): \(\epsilon_{\text{mse}} = \frac{1}{N \cdot T^*} \sum (y_i – \hat{y}_i)^2\)
- Mean Absolute Percentage Error (MAPE): \(\epsilon_{\text{mape}} = \frac{1}{N \cdot T^*} \sum \frac{|y_i – \hat{y}_i|}{y_i} \times 100\%\)
- Maximum Squared Error (Max SE): \(\epsilon_{\text{max}} = \max(y_i – \hat{y}_i)^2\) (indicates worst-case performance).
- MSE for the Fastest-Charging Cell (\(\epsilon_{\text{fast}}\)): The cell that reaches full charge first is often most vulnerable to overcharging; accurate estimation for this energy storage cell is particularly safety-critical.
The CMCF network was compared against three established data-driven methods adapted to the multi-cell setting by training one model per cell: Support Vector Regression (SVR), a standard Multi-Layer Perceptron (MLP), and a Long Short-Term Memory network (LSTM). All models were trained and tested under identical conditions.
Results and Analysis
The quantitative results, presented in the table below, demonstrate the significant superiority of the CMCF approach. It outperforms all benchmark methods across every single metric by a considerable margin.
| Method | \(\epsilon_{\text{mse}}\) (×10-3) | \(\epsilon_{\text{mape}}\) (%) | \(\epsilon_{\text{max}}\) (×10-2) | \(\epsilon_{\text{fast}}\) (×10-3) |
|---|---|---|---|---|
| SVR | 6.61 | 13.34 | 8.27 | 9.30 |
| MLP | 1.10 | 5.39 | 1.50 | 0.587 |
| LSTM | 0.531 | 3.33 | 1.03 | 1.50 |
| CMCF (Proposed) | 0.152 | 1.72 | 0.370 | 0.187 |
The CMCF network reduces the overall MSE by at least 71.4% compared to the best benchmark (LSTM). More importantly, it drastically lowers the maximum error (\(\epsilon_{\text{max}}\)) by 64%, indicating more robust and reliable estimates for all energy storage cells, even outliers. The accuracy for the fastest-charging cell is also significantly improved, which is crucial for preventing overcharge in the most vulnerable energy storage cell of the cluster.
Ablation Studies
To validate the contribution of each key component in the CMCF architecture, we conducted ablation studies. The results are summarized in the following table.
| Ablated Model | Description | \(\epsilon_{\text{mse}}\) (×10-3) |
|---|---|---|
| w/o Cluster Features | Uses only cell features, no global cluster input. | 2.99 |
| w/o Memory Module | Removes the memory module; uses cell and cluster features. | 0.236 |
| w/o Cluster-Attention | Replaces attention fusion with simple concatenation. | 0.336 |
| w/o CF & Memory | Uses only cell features (baseline deep model). | 0.594 |
| Full CMCF | The complete proposed architecture. | 0.152 |
The ablation results clearly show that every component is essential. The removal of Cluster Features causes the most severe performance degradation, underscoring the vital importance of global cluster context for estimating individual energy storage cell states. Removing the Memory Module or the Cluster-Attention fusion also leads to noticeable increases in error, confirming their roles in learning cell-specific patterns and effectively integrating multi-perspective information. The full CMCF model achieves the lowest error, demonstrating the synergistic effect of its integrated design.
Conclusion and Future Work
Accurate per-cell State-of-Charge estimation within an energy storage cell cluster is a fundamental requirement for the safe, efficient, and reliable operation of modern battery energy storage systems. This work presents the CMCF network, a novel deep learning solution specifically designed for this challenging multi-cell estimation problem. By innovatively combining a dual-perspective input (cell-level and cluster-level), a trainable memory mechanism for capturing prototypical cell patterns and disparities, and an attention-based feature fusion strategy, the CMCF network achieves a fine-grained and highly accurate estimation of SOC for every energy storage cell in a cluster.
Experimental validation on real-world operational data from a large LFP battery cluster demonstrates its superior performance compared to conventional data-driven methods, with a reduction in overall estimation error exceeding 71%. The ablation studies provide strong evidence for the efficacy of each architectural component. The CMCF framework offers a powerful and practical tool for next-generation BMS, enhancing safety by providing precise visibility into the state of each individual energy storage cell, which is paramount for preventing failures and optimizing cluster performance.
Future work will focus on extending the CMCF framework to jointly estimate other critical states, such as State of Health (SOH) and State of Power (SOP), and to adapt dynamically to the ongoing aging and divergence of energy storage cells within the cluster throughout their entire operational lifetime.