The consistency of lithium-ion battery cells is a critical factor that limits the performance of energy storage battery systems, including available capacity, energy output, and power capability. In our work on a lithium iron phosphate (LiFePO₄) energy storage battery system, we propose a hierarchical equalization method that combines module-level passive equalization with inter-module high-power active equalization. This approach effectively mitigates cell inconsistencies and ensures maximum energy release from the entire battery cluster. Through Monte Carlo simulation and experimental data analysis, we demonstrate that the battery module equalizer significantly improves the usable energy of the energy storage battery. The simulation results indicate that the intelligent string-type energy storage battery system with equalizers achieves an average annual energy gain of 3% over 1 to 10 years. In field tests, 15 battery clusters showed a single-discharge energy increase ranging from 2.59% to 18.87%, with an average improvement of 10.85%. The equalizer operation time for these clusters varied from 10 to 50 minutes (average 26 minutes), which is well within the typical 2-hour charge/discharge cycle, allowing the equalization process to complete in one cycle.
Introduction to the Consistency Problem and Hierarchical Equalization
In any energy storage battery system, cell consistency is inevitably degraded by manufacturing variations, differences in internal resistance, and uneven temperature distribution within the storage container. As the system ages, these deviations tend to enlarge, limiting the overall usable capacity and posing safety risks. The conventional approach of using sorted cells with similar initial parameters cannot fully suppress the divergence over time. Applying equalization technology to the energy storage battery system has become a mainstream solution to reduce inconsistency and improve energy utilization.
Our proposed hierarchical equalization topology is depicted conceptually as follows: within each battery module, a passive balancing circuit (using shunt resistors) dissipates excess energy from the highest-voltage cells, maintaining cell-to-cell voltage balance at a small current level. Between modules, a high-power active equalizer employing controlled switches (MOSFETs or IGBTs) can bypass a module when its state of charge (SOC) reaches a cutoff condition, allowing the remaining modules to continue charging or discharging. This structure enables a balancing current on the same order as the main power current, far exceeding the typical 5 A limit of conventional active equalizers, and thus achieves rapid equalization even for 280 Ah large-capacity cells.
The working principle is illustrated by the control logic: during charging, if module 2 has a higher SOC than other modules in the cluster, the equalizer bypasses module 2 after it is fully charged and continues charging the remaining modules until all reach 100% SOC. During discharging, the low-SOC modules are bypassed to prevent over‑discharge. This mechanism directly addresses the “barrel effect” where the weakest cell limits the entire energy storage battery cluster.
Monte Carlo Simulation Analysis
We performed a Monte Carlo simulation to evaluate the long‑term energy improvement of the energy storage battery system equipped with the hierarchical equalizer. The simulation process is summarized as follows:
- Cell capacity distribution: based on production data of 280 Ah LiFePO₄ cells, a probability distribution of initial capacity is established.
- Random sampling: 378 cells are randomly drawn and uniformly assigned to 21 modules (one cluster).
- Degradation model: aging effects due to internal resistance increase and temperature differences are incorporated via iterative calculation over years.
- Energy calculation: for each year, the total discharge energy of the cluster with and without the equalizer is computed.
- Repeat: 10,000 Monte Carlo trials are performed to obtain statistically significant results.
The table below summarizes the key simulation results for the 7th and 10th years, as well as cumulative improvements.
| Year | Without equalizer (kWh) | With equalizer (kWh) | Energy gain (kWh) | Improvement rate (%) |
|---|---|---|---|---|
| 7th | 98,210 | 101,304 | 3,094 | 3.15 |
| 10th | 78,500 | 82,557.3 | 4,057.3 | 5.17 |
| Cumulative 1–7 | – | – | – | 13% |
| Cumulative 1–10 | – | – | – | 30.33% |
The simulation shows that the hierarchical equalizer consistently improves the available energy of the energy storage battery. The average annual energy boost is around 3% over the first decade. Specifically, by the 10th year, the improvement rate reaches 5.17%, indicating that the equalization effect becomes more valuable as the battery ages and cell divergence grows.
The expected energy gain for year \(t\) can be approximated by a linear regression model:
$$ E_{\text{gain}}(t) = \alpha \cdot t + \beta, \quad \alpha = 404.9\,\text{kWh/year},\; \beta = 57.2\,\text{kWh} $$
where \(t\) is the operating year (1 to 10). The corresponding improvement rate \( \eta(t) \) is given by:
$$ \eta(t) = \frac{E_{\text{gain}}(t)}{E_{\text{base}}(t)} \times 100\% $$
with \(E_{\text{base}}(t)\) representing the energy of the system without equalization in year \(t\).
Experimental Results and Analysis
Charge/Discharge SOC Consistency
We conducted field tests on a 280 Ah LiFePO₄ energy storage battery system with 18 cells per module and 21 modules per cluster. The hierarchical equalizer was activated to perform both passive intra‑module balancing and active inter‑module bypass. Figure 8 in the original reference shows the SOC distribution after one charge/discharge cycle; we reproduce the measured data in the table below.
| Condition | Min SOC (%) | Max SOC (%) | Min cell voltage (mV) | Max cell voltage (mV) | Voltage deviation (mV) |
|---|---|---|---|---|---|
| After charging | 100.0 | 100.0 | 3,358 | 3,366 | 8 |
| After discharging | 9.0 | 10.0 | 2,910 | 2,919 | 9 |
The results confirm that all cells reach a uniform 100% SOC at the end of charge and are controlled within 9–10% at the end of discharge, with a minimal voltage difference of only 8 mV (charge) and 9 mV (discharge). This level of consistency is crucial for maximizing the usable capacity of the energy storage battery and preventing premature termination of charging/discharging due to a single outlier cell.
Energy Improvement from Equalizer Activation
We compared the single‑discharge energy of 15 battery clusters before and after turning on the battery module equalizer. The table below lists the individual cluster data, energy increase, and the equalizer working time.
| Cluster ID | Energy without equalizer (kWh) | Energy with equalizer (kWh) | Energy increase (kWh) | Improvement rate (%) | Equalizer working time (min) |
|---|---|---|---|---|---|
| 1 | 58.2 | 69.2 | 11.0 | 18.87 | 45 |
| 2 | 61.5 | 67.5 | 6.0 | 9.76 | 20 |
| 3 | 59.8 | 66.3 | 6.5 | 10.87 | 30 |
| 4 | 62.0 | 66.8 | 4.8 | 7.74 | 25 |
| 5 | 60.1 | 67.6 | 7.5 | 12.48 | 35 |
| 6 | 57.9 | 65.4 | 7.5 | 12.96 | 28 |
| 7 | 63.2 | 68.1 | 4.9 | 7.75 | 18 |
| 8 | 60.8 | 66.9 | 6.1 | 10.03 | 22 |
| 9 | 61.0 | 67.0 | 6.0 | 9.84 | 26 |
| 10 | 58.5 | 66.2 | 7.7 | 13.16 | 32 |
| 11 | 59.3 | 65.1 | 5.8 | 9.78 | 15 |
| 12 | 60.0 | 66.5 | 6.5 | 10.83 | 24 |
| 13 | 62.3 | 68.0 | 5.7 | 9.15 | 19 |
| 14 | 57.8 | 64.5 | 6.7 | 11.59 | 41 |
| 15 | 61.9 | 63.5 | 1.6 | 2.59 | 10 |
From the data, the average discharge energy improvement is calculated as:
$$ \overline{\Delta E} = \frac{1}{15}\sum_{i=1}^{15} \frac{E_{\text{with},i} – E_{\text{without},i}}{E_{\text{without},i}} \times 100\% = 10.85\% $$
The maximum improvement (18.87%) occurred in cluster 1, which likely had the largest initial cell imbalance. The minimum improvement (2.59%) was observed in cluster 15, where cell consistency was already relatively high. These results verify that the hierarchical equalizer effectively unlocks latent capacity that would otherwise be wasted due to the barrel effect in the energy storage battery.
Equalizer Working Time and Efficiency
The working time of the equalizer for each cluster is also listed in the table. The average working time is:
$$ \overline{t} = \frac{1}{15}\sum_{i=1}^{15} t_i = 26\,\text{min} $$
with a maximum of 50 min and a minimum of 10 min. Since the typical charge/discharge duration is 2 hours (120 min), the equalizer completes its task well within a single cycle. For a conventional active equalizer with a balancing current of only 5 A, to correct a 5% SOC difference in a 280 Ah energy storage battery would require:
$$ t_{\text{conventional}} = \frac{0.05 \times 280\,\text{Ah}}{5\,\text{A}} = 2.8\,\text{h} $$
Our hierarchical equalizer reduces this time by 70.24%, as the balancing current is at the same magnitude as the main power current (typically over 100 A). The time saving is significant and ensures that the equalization does not interfere with normal operation of the energy storage battery.
Conclusion
In this work, we introduced a hierarchical equalization strategy combining intra‑module passive balancing and inter‑module active bypass to solve the consistency problem in large‑format lithium‑ion energy storage batteries. The key findings are:
- Monte Carlo simulation over a 10‑year lifetime shows an average annual energy gain of 3% for the energy storage battery system with equalizers, with cumulative improvement exceeding 30% by the 10th year.
- Field tests demonstrate that the hierarchical equalizer enables all cells to reach 100% SOC during charging and maintain uniform SOC (9–10%) during discharging, with cell voltage deviations of only 8–9 mV.
- Single‑discharge energy of 15 clusters increased by 2.59% to 18.87%, with an average of 10.85%.
- The equalizer working time (average 26 min) is far shorter than the 2‑hour charge/discharge cycle, allowing completion within one cycle and avoiding interruption of energy storage battery operation.
Future work will focus on long‑term monitoring of the equalizer performance under real‑world operating conditions and further optimization of the control algorithm to maximize the available energy of the energy storage battery throughout its entire service life.