In recent years, the rapid development of renewable energy systems has heightened the importance of energy storage technologies, particularly those involving energy storage cells. As a key component, energy storage cells, such as lithium-ion batteries, play a critical role in stabilizing power grids and managing energy fluctuations. However, the operation data collected by battery management systems (BMS) often suffer from low quality, complex operating conditions, incomplete charge-discharge cycles, and multi-source heterogeneity. These issues pose significant challenges for accurate state estimation and fault prediction in energy storage systems. In this paper, I address these problems by investigating the mechanisms and methods for splicing and reconstructing operation data of energy storage cells. By leveraging gradient descent algorithms and analyzing transient and steady-state characteristics during operational shifts, I propose a novel approach that enhances data continuity and accuracy. This method not only improves the reliability of data-driven models but also facilitates advanced applications like state of health (SOH) estimation. Throughout this work, the term “energy storage cell” is emphasized to underscore its centrality in energy storage systems, and I will explore various aspects, including mathematical formulations, empirical boundaries, and validation through experimental and real-world data.
The splicing and reconstruction of energy storage cell operation data are essential for developing robust data-driven models. Traditional methods, such as polynomial fitting or equivalent circuit models, often introduce artificial errors and noise, leading to reduced precision. In contrast, my approach focuses on the intrinsic mechanisms of energy storage cells during operation, utilizing gradient descent optimization to derive empirical mathematical equations and boundary conditions. For instance, the loss function for data splicing can be defined as follows: Let \(X = \{x_1, x_2, \dots, x_m\}\) represent a collection of data points from multiple fragments. The loss function \(J(X)\) is formulated as:
$$J(X) = \sum_{i=1}^{m} \max(0, |x_i – x_{i-1}| – p)^2$$
where \(p\) is the boundary value at the splicing point. This function helps minimize discrepancies between adjacent data fragments. The gradient of this loss function is computed as:
$$\frac{\partial J}{\partial x_i} = 2(|x_i – x_{i-1}| – p) \cdot \text{sign}(x_i – x_{i-1})$$
Using gradient descent, the parameters are updated iteratively:
$$x_i^{(t+1)} = x_i^{(t)} – \alpha \frac{\partial J}{\partial x_i}$$
where \(\alpha\) is the learning rate and \(t\) denotes the iteration step. This optimization process ensures that the splicing points align with the operational characteristics of energy storage cells, such as voltage, current, and capacity consistency.
To further elucidate the mechanisms, I have established key empirical equations and boundary conditions based on extensive statistical analysis of energy storage cell data. These include requirements for current, cumulative charge/discharge capacity, voltage, voltage change rate, and transient duration. For example, the current difference between adjacent data fragments must satisfy:
$$I_d = I_{\text{front}} – I_{\text{back}} \leq 5 \, \text{A}$$
where \(I_{\text{front}}\) and \(I_{\text{back}}\) are the current values of the preceding and succeeding fragments, respectively. This condition ensures that current amplitudes do not cause abrupt changes in reconstructed data. Similarly, the cumulative charge/discharge capacity at splicing points must adhere to:
$$C_d = C_{\text{front}}^{\text{end}} – C_{\text{back}}^{\text{start}} = 0$$
This guarantees energy conservation and data continuity. Voltage consistency is another critical factor, with the boundary condition:
$$U_d = U_{\text{front}}^{\text{end}} – U_{\text{back}}^{\text{start}} \leq 0.005 \, \text{V}$$
Moreover, the rate of voltage change must be smooth, as defined by:
$$k_d = k_{\text{front}}^{\text{end}} – k_{\text{back}}^{\text{start}} \leq 0.0001$$
where \(k\) represents the voltage change rate. Transient duration during operational shifts, such as from charging to discharging, is also considered. Based on empirical data, the transient time \(T\) follows:
$$T_{\text{max}} = 96 \, \text{s}, \quad T_{\text{min}} = 61 \, \text{s}, \quad T_{\text{mean}} = 79.82 \, \text{s}$$
and data splicing should only occur after \(T \geq T_{\text{max}}\) to avoid transient effects. These conditions collectively ensure that the spliced and reconstructed data accurately reflect the behavior of energy storage cells under various operational scenarios.
The methodology for splicing and reconstructing energy storage cell operation data involves a systematic process consisting of six main steps. First, data acquisition is performed using sensors in BMS or monitoring devices in energy storage systems to collect key parameters like current, voltage, and cumulative capacity over time. Second, data fragments are divided based on time intervals, current rates, or operational shifts, ensuring each fragment represents a stable, single-mode operation. Third, data cleaning and preprocessing are applied to remove anomalies, noise, and missing values through interpolation techniques. Fourth, data splicing and reconstruction are executed by aligning fragments according to the established boundary conditions, using algorithms like gradient descent to optimize continuity. The flowchart for this step includes fragment selection, boundary checks, and iterative optimization. Fifth, the reconstructed curves are refined using mathematical, physical, or machine learning models, such as Kalman filters, equivalent circuit models, or support vector machines, to enhance smoothness and accuracy. Finally, the spliced data are validated through statistical analysis, error metrics, and practical applications to assess performance. For instance, error indicators like root mean square error (RMSE) and mean absolute error (MAE) are calculated to quantify accuracy.
To validate the proposed mechanisms and methods, I applied them to various datasets, including hybrid pulse power characterization (HPPC) tests, reference performance tests (RPT), and real-world operational data from energy storage plants. In HPPC tests, which evaluate dynamic responses of energy storage cells, the discharge voltage curves were spliced and reconstructed. The original fragmented data were transformed into a continuous discharge curve, demonstrating high consistency. Statistical analysis of transient durations from HPPC data yielded values like \(T_{\text{min}} = 61 \, \text{s}\) and \(T_{\text{max}} = 96 \, \text{s}\), which informed the splicing criteria. Similarly, RPT data involving charging voltage curves under different temperatures and cycle counts were successfully reconstructed from randomly split fragments, showing the method’s robustness across varying conditions. The results confirmed that the spliced curves maintained voltage and current continuity, with errors within acceptable limits. For example, the voltage difference at splicing points was consistently below 0.005 V, aligning with the empirical boundaries.
In real-world engineering applications, the splicing and reconstruction method was tested on data from energy storage stations performing peak shaving and frequency regulation. For instance, in a peak shaving scenario, voltage curves from multiple fragments were reconstructed into continuous profiles, with current rates around 0.5 C and state of energy (SOE) ranging from 41% to 83%. The table below summarizes empirical values derived from these applications, highlighting key parameters for energy storage cell operation data:
| Parameter | Range |
|---|---|
| Voltage (V) | 3.307–3.68 |
| Current (A) | 2.5–136.4 |
| SOE (%) | 41–83 |
| Duration (s) | 100–1220 |
These values provide practical guidelines for implementing data splicing in energy storage systems. Additionally, in frequency regulation cases, data from battery clusters with 240 cells were reconstructed, showing seamless integration of fragments under dynamic loads. The success in these scenarios underscores the method’s adaptability to complex operational environments for energy storage cells.
Beyond validation, the splicing and reconstruction technique has significant engineering applications, particularly in health state estimation for energy storage cells. By combining with incremental capacity analysis (ICA), which relies on complete charge-discharge curves, the method enables accurate SOH estimation. ICA analyzes the relationship between voltage and capacity during charging, where the peak area in incremental capacity curves correlates with battery degradation. The SOH is calculated as:
$$S_{\text{health}} = \frac{Q_{\text{now}}}{Q_{\text{start}}} \times 100\%$$
where \(Q_{\text{now}}\) is the current mid-range capacity and \(Q_{\text{start}}\) is the initial value. However, real-world data often lack full cycles, necessitating splicing to form complete curves. The process involves: (1) reconstructing data fragments into continuous profiles, (2) identifying voltage points \(u_1\) and \(u_2\) from initial ICA curves, (3) computing the area under the curve between these points for \(Q_{\text{now}}\), and (4) deriving SOH. This approach was applied to operational data, resulting in reliable SOH estimates with errors below 2%, demonstrating the practical value of data splicing for energy storage cell management.
In conclusion, this paper thoroughly investigates the splicing and reconstruction of energy storage cell operation data, presenting mechanisms based on gradient descent optimization and empirical boundary conditions. The proposed method effectively addresses data fragmentation issues in BMS, enhancing the quality and continuity of datasets for energy storage cells. Validation through HPPC, RPT, and real-world data confirms the method’s high accuracy and adaptability, with key empirical values like transient durations and voltage limits providing actionable insights. Furthermore, the integration with ICA for SOH estimation highlights its engineering relevance, enabling improved state evaluation and fault prediction. Future work could explore adaptive learning algorithms for dynamic operational conditions, further advancing the reliability of energy storage systems. Throughout this research, the focus on energy storage cells has been paramount, emphasizing their role in achieving efficient and sustainable energy storage solutions.
The implications of this study extend to various aspects of energy storage cell management. For instance, the mathematical formulations derived here can be integrated into BMS software for real-time data processing. Consider the general equation for data consistency in energy storage cells:
$$F(X) = \sum_{i=1}^{n} w_i \cdot f_i(x_i)$$
where \(w_i\) are weights assigned to different parameters like voltage or current, and \(f_i\) are functions representing operational constraints. This can be optimized using machine learning techniques, such as reinforcement learning, to handle non-linearities in energy storage cell behavior. Additionally, the table below summarizes the boundary conditions for splicing energy storage cell data, reinforcing the empirical foundations:
| Parameter | Condition | Value |
|---|---|---|
| Current Difference | \(I_d \leq\) | 5 A |
| Voltage Difference | \(U_d \leq\) | 0.005 V |
| Capacity Difference | \(C_d =\) | 0 |
| Voltage Change Rate | \(k_d \leq\) | 0.0001 |
| Transient Duration | \(T \geq\) | 96 s |
These conditions ensure that spliced data for energy storage cells maintain physical consistency and energy conservation. As energy storage cells become increasingly integral to smart grids and renewable integration, methods like these will be crucial for optimizing their performance and lifespan. The continuous emphasis on energy storage cells throughout this work underscores their importance in the evolving energy landscape, and I believe that advancements in data splicing will pave the way for more intelligent and resilient energy storage systems.