Our team has developed a novel method for evaluating the consistency of energy storage battery stacks used in large-scale energy storage power stations. The challenge we addressed is the vast and multidimensional nature of operational data collected from these stations, which includes voltage, internal resistance, state of charge (SOC), and temperature. Traditional evaluation methods often rely on single-dimensional metrics or subjective weighting schemes, leading to incomplete or biased assessments. Our approach integrates multi-dimensional data fusion, an improved grey relational analysis, and K-medoids clustering to provide a more robust, objective, and granular evaluation of energy storage battery health.
The evaluation framework we designed is built upon four pillars of energy storage battery performance: voltage, internal resistance, state of charge (SOC), and temperature. For each of these dimensions, we calculate three statistical indicators: standard deviation, coefficient of variation, and range. This results in a comprehensive set of 12 features that capture both the absolute and relative dispersion of key battery parameters. The table below summarizes the indicators we selected for evaluating energy storage battery consistency.
| Dimension | Indicator | Mathematical Formula | Interpretation |
|---|---|---|---|
| Voltage | Standard Deviation | $$ \sigma_{U} = \sqrt{\frac{\sum_{i=1}^{n}(U_i – \bar{U})^2}{n}} $$ | Measures the dispersion of cell voltages. |
| Coefficient of Variation | $$ CV_U = \frac{\sigma_U}{\bar{U}} $$ | Normalizes dispersion by the mean voltage. | |
| Range | $$ \Delta U = U_{max} – U_{min} $$ | Captures the extreme difference in cell voltages. | |
| Internal Resistance | Standard Deviation | $$ \sigma_R = \sqrt{\frac{\sum_{i=1}^{n}(R_i – \bar{R})^2}{n}} $$ | Measures the dispersion of internal resistance. |
| Coefficient of Variation | $$ CV_R = \frac{\sigma_R}{\bar{R}} $$ | Normalized measure of resistance variation. | |
| Range | $$ \Delta R = R_{max} – R_{min} $$ | Shows the maximum spread in resistance values. | |
| SOC | Standard Deviation | $$ \sigma_{SOC} = \sqrt{\frac{\sum_{i=1}^{n}(SOC_i – \bar{SOC})^2}{n}} $$ | Indicates dispersion of remaining capacity. |
| Coefficient of Variation | $$ CV_{SOC} = \frac{\sigma_{SOC}}{\bar{SOC}} $$ | Normalized SOC dispersion. | |
| Range | $$ \Delta SOC = SOC_{max} – SOC_{min} $$ | Identifies potential charge imbalance extremes. | |
| Temperature | Standard Deviation | $$ \sigma_T = \sqrt{\frac{\sum_{i=1}^{n}(T_i – \bar{T})^2}{n}} $$ | Measures thermal dispersion across cells. |
| Coefficient of Variation | $$ CV_T = \frac{\sigma_T}{\bar{T}} $$ | Normalized temperature variation. | |
| Range | $$ \Delta T = T_{max} – T_{min} $$ | Shows the thermal gradient’s worst-case scenario. |
To determine the relative importance of these 12 indicators, we employed an improved grey relational analysis. The traditional grey relational method requires the selection of a resolution coefficient \(\rho\), often set to 0.5 by default. This introduces a degree of subjectivity and can lead to disproportionate weight distribution, especially when dealing with a larger number of indicators. Our innovation replaced the traditional distance metric with the Mahalanobis distance. This approach is advantageous because the Mahalanobis distance accounts for correlations between variables and is scale-invariant, thus eliminating the need for the subjective resolution coefficient and the burden of indicator normalization.
The weighting process is as follows. We first constructed a comparison data matrix \(\mathbf{E}\) from expert judgments or historical data. The reference sequence \(\mathbf{E}_0\) was defined as the vector of maximum values for each indicator across all experts, representing the ideal state. We then calculated the Mahalanobis distance between each comparison sequence \(\mathbf{E}_k\) and the reference sequence \(\mathbf{E}_0\):
$$ D_m(\mathbf{E}_0, \mathbf{E}_k) = \sqrt{(\mathbf{E}_0 – \mathbf{E}_k)^T \mathbf{\Sigma}^{-1} (\mathbf{E}_0 – \mathbf{E}_k)} $$
where \(\mathbf{\Sigma}\) is the covariance matrix of the combined matrix \(\mathbf{E}’ = [\mathbf{E}_0, \mathbf{E}_1, …, \mathbf{E}_i]\). The weight for each indicator \(k\) was then derived from:
$$ \omega’_k = \frac{1}{1 + D_m(\mathbf{E}_0, \mathbf{E}_k)} $$
Finally, these weights were normalized to sum to 1:
$$ \omega_k = \frac{\omega’_k}{\sum_{j=1}^{n} \omega’_j} $$
This method yielded a set of weights that objectively reflected the discriminatory power and relevance of each indicator, as shown in the table below. Notably, SOC and voltage-related indicators received the highest weights, followed by temperature, while internal resistance indicators had relatively lower weights. This suggests that SOC and voltage variations are the most critical factors for capturing inconsistencies in the energy storage battery stack under normal operating conditions.
| Indicator | Weight |
|---|---|
| SOC Standard Deviation | 0.113083 |
| SOC Coefficient of Variation | 0.087621 |
| SOC Range | 0.071971 |
| Voltage Standard Deviation | 0.098903 |
| Voltage Coefficient of Variation | 0.080828 |
| Voltage Range | 0.073921 |
| Internal Resistance Standard Deviation | 0.078036 |
| Internal Resistance Coefficient of Variation | 0.078072 |
| Internal Resistance Range | 0.072279 |
| Temperature Standard Deviation | 0.090071 |
| Temperature Coefficient of Variation | 0.073197 |
| Temperature Range | 0.082019 |
To segment the continuously monitored data into discrete performance levels, we selected the K-medoids clustering algorithm. Unlike K-means, which uses the mean of points as a cluster center (centroid), K-medoids uses an actual data point as the center (medoid). This makes the algorithm significantly more robust to outliers and noise, which are common in real-world sensor data from energy storage battery systems. The algorithm iteratively assigns each data point to the nearest medoid and then updates the medoids to minimize the total dissimilarity within each cluster.
Our evaluation process, illustrated in the workflow diagram, begins with extracting raw consistency indicators from historical data. These indicators are first positively normalized so that a higher value always indicates better consistency. We then calculate the weighted sum of these normalized indicators using the weights derived from the improved grey relational analysis. The weighted data points are subsequently clustered using K-medoids into several distinct groups. The cluster with the highest average weighted score is assigned the best performance grade (e.g., Grade 1), and the cluster with the lowest score is assigned the worst performance grade (e.g., Grade 4). This automatic, data-driven grading system allows for efficient monitoring of the energy storage battery stack over time.
We validated our method using operational data from a real-world energy storage power station. The dataset comprised 1,000 consecutive operational records from two different battery stacks (designated A and B), containing voltage, SOC, temperature, and internal resistance readings. After preprocessing and weight calculation, we performed K-medoids clustering with \(k=4\) to partition the operational states into four consistency grades. The clustering results for battery stacks A and B are presented in the tables below, showing the cluster centers’ coordinates and the subsequent grading.
| Indicator / Cluster | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 |
|---|---|---|---|---|
| SOC Std Dev | 0.382709 | 0.485880 | 0.979470 | 0.964935 |
| SOC CV | 0.980564 | 0.975476 | 0.997670 | 0.998306 |
| SOC Range | 0.197628 | 0.275178 | 0.956022 | 0.907441 |
| Voltage Std Dev | 0.881706 | 0.863472 | 0.890888 | 0.901270 |
| Voltage CV | 0.999814 | 0.999784 | 0.999823 | 0.999845 |
| Voltage Range | 0.769230 | 0.714285 | 0.769230 | 0.769230 |
| Resistance Std Dev | 0.999106 | 0.999106 | 0.999106 | 0.999106 |
| Resistance CV | 0.995512 | 0.995512 | 0.995512 | 0.995512 |
| Resistance Range | 0.998003 | 0.998003 | 0.998003 | 0.998003 |
| Temp Std Dev | 0.837219 | 0.572695 | 0.759035 | 0.647705 |
| Temp CV | 0.993147 | 0.977301 | 0.989194 | 0.977609 |
| Temp Range | 0.662251 | 0.345901 | 0.548546 | 0.406338 |
| Number of Points | 100 | 396 | 263 | 241 |
| Weighted Score | 0.711440 | 0.701358 | 0.834663 | 0.820372 |
| Performance Grade | 3 | 4 | 1 | 2 |
For Battery Stack A, the K-medoids clustering effectively separated the data into four distinct groups. Cluster 3, representing 263 data points, achieved the highest weighted score of 0.834663 and was assigned Grade 1. This cluster demonstrated excellent SOC and temperature consistency. In contrast, Cluster 2, with the lowest score of 0.701358, was assigned Grade 4 and showed poor performance, particularly in SOC and temperature ranges. The voltage and internal resistance consistency remained relatively stable and high across all clusters. This suggests that for this specific battery stack, variations in SOC and temperature are the primary drivers of overall inconsistency.
| Indicator / Cluster | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 |
|---|---|---|---|---|
| SOC Std Dev | 0.659617 | 0.737647 | 0.556009 | 0.741762 |
| SOC CV | 0.973187 | 0.964539 | 0.961286 | 0.965109 |
| SOC Range | 0.440334 | 0.540540 | 0.331016 | 0.524934 |
| Voltage Std Dev | 0.776338 | 0.805910 | 0.785014 | 0.805910 |
| Voltage CV | 0.999630 | 0.999686 | 0.999639 | 0.999686 |
| Voltage Range | 0.625000 | 0.666666 | 0.666666 | 0.666666 |
| Resistance Std Dev | 0.998359 | 0.996739 | 0.997042 | 0.998214 |
| Resistance CV | 0.991843 | 0.983764 | 0.985341 | 0.991099 |
| Resistance Range | 0.996015 | 0.993048 | 0.993048 | 0.995024 |
| Temp Std Dev | 0.678283 | 0.844485 | 0.738270 | 0.856525 |
| Temp CV | 0.981949 | 0.986718 | 0.980144 | 0.987954 |
| Temp Range | 0.463392 | 0.693962 | 0.521648 | 0.697836 |
| Number of Points | 308 | 423 | 161 | 108 |
| Weighted Score | 0.793646 | 0.848192 | 0.786182 | 0.849907 |
| Performance Grade | 3 | 2 | 4 | 1 |
Battery Stack B’s clustering results showed a different profile. The overall scores were more tightly clustered than in Stack A. Clusters 2 and 4 were grades 2 and 1, respectively, and showed better temperature consistency. The worst-performing cluster was Cluster 3 (Grade 4), which exhibited the poorest SOC consistency. This analysis allows operators to see that Stack B’s main weakness lies in SOC management, whereas Stack A’s issues are more related to both SOC and temperature.
After grading, we performed a deeper analysis on the lowest-performing cluster for each battery stack to identify potential faults. For Stack A, the Grade 4 data (Cluster 2) was re-clustered. The worst sub-cluster within it, representing 131 data points, occurred on January 23, 2024, between 3:00 and 9:00. Further investigation revealed this coincided with a long charging phase followed by a rest period. During the charging phase, SOC values rose at different rates across the battery clusters, increasing dispersion. This was followed by a rest period where the SOC dispersion remained elevated. While the consistency was poor, it was attributable to the normal system dynamics of charging and resting, and the SOC standard deviation and range values remained within typical operational thresholds.
A more critical scenario was found in the worst sub-cluster of Battery Stack B, which contained 26 data points from January 23, 2024, between 3:05 and 5:10. As shown in the table below, this sub-cluster (Cluster 2) had alarmingly low values for SOC standard deviation and SOC range, with a SOC range score of only 0.034299.
| Indicator / Cluster | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 |
|---|---|---|---|---|
| SOC Std Dev | 0.895513 | 0.077354 | 0.512050 | 0.556009 |
| SOC Range | 0.776398 | 0.034299 | 0.307314 | 0.331016 |
| Voltage Std Dev | 0.785015 | 0.800642 | 0.749252 | 0.785015 |
| Temp Std Dev | 0.741641 | 0.756582 | 0.711064 | 0.738271 |
| Number of Points | 49 | 26 | 9 | 77 |
| Weighted Score | 0.861446 | 0.703148 | 0.764323 | 0.786182 |
| Ranking | 1 | 4 | 3 | 2 |
A score of 0.034 for the SOC range indicates that the battery stack experienced a period of extreme and abnormal SOC divergence. By tracing back the raw data, we discovered that one specific battery cluster (Cluster 5) within the stack showed anomalous behavior. At 3:05, while all other clusters in the stack began to charge and their SOCs increased, the SOC of Cluster 5 began to drop. It continued to diverge from the others for the next hour, reaching its maximum deviation around 4:40. The SOC imbalance only began to correct itself after 4:45, finally returning to a normal state by 5:35. We believe this event was highly indicative of a fault, likely related to a malfunction in the SOC equalization control system for that particular cluster, which may have caused an internal circulating current. This diagnosis provides a clear and urgent target for maintenance intervention.
In conclusion, our team has developed a comprehensive and effective methodology for evaluating the consistency of energy storage battery stacks. By fusing multi-dimensional data and applying an objective weighting method, we can generate a nuanced performance grade for any given time period. The K-medoids algorithm proved to be a powerful tool for distinguishing between normal operational variations and genuine anomalies. The case study on Battery Stack B successfully demonstrated the method’s potential for early fault detection, identifying a specific, time-constrained event that was likely caused by an equipment malfunction. Our method moves beyond simple pass/fail assessments to provide a structured, data-driven system that helps operators understand the state of their energy storage battery assets, pinpoint weaknesses, and perform targeted preventative maintenance. This can significantly enhance the safety, reliability, and longevity of the entire energy storage system.