In recent years, the rapid development of renewable energy generation technologies and the global push for carbon neutrality have made energy storage systems a critical solution for addressing issues like wind and solar power curtailment. Among various energy storage technologies, the energy storage lithium battery has gained widespread adoption due to its long lifespan, high flexibility, and efficiency in high-voltage direct current (DC) applications, such as electric vehicles, hybrid electric vehicles, and microgrids. However, in large-scale energy storage lithium battery systems, inconsistencies in battery parameters among modules can lead to imbalances in the state of charge (SOC), resulting in overcharging or over-discharging, which may cause internal damage to battery cells. Therefore, achieving SOC balancing is essential for improving battery utilization and ensuring the safe and stable operation of energy storage lithium battery systems.
The new generation of energy storage lithium battery systems focuses on power electronics-based battery pack technology, where battery modules are cascaded with modular power converters to form battery power modules. This allows independent control of the charge and discharge currents for each battery module, effectively mitigating inconsistencies in series and parallel configurations. In such systems, the output sides of the modules are connected in series and integrated into a DC grid. However, in grid-connected operation, the DC bus voltage is fixed, necessitating stable power distribution among the modules based on power commands while achieving SOC balancing. Research has shown that when module controllers independently perform current control, the system exhibits self-stability in discharge mode but suffers from current instability and diverging bus-side voltages in charge mode. This paper addresses these challenges by proposing novel control strategies for power distribution and SOC balancing in energy storage lithium battery systems.
The system under study consists of multiple battery cells connected in series to form a battery module, with each module cascaded a two-phase interleaved bidirectional DC-DC converter. The output sides of these converters are connected in series and integrated into a DC grid. In this configuration, the output current of each module is equal to the cluster current on the bus side, denoted as \( I_o \). The bus-side voltage and current for the \( i \)-th module are represented as \( U_{busi} \) and \( I_{busi} \), respectively, while the battery module voltage is \( U_{Bi} \). The power relationship between the battery side and the bus side, neglecting losses, is given by:
$$ I_{Bi} = \frac{U_{busi} I_{busi}}{U_{Bi}} $$
In discharge mode, the DC-DC converter operates in boost mode, and the relationship between the bus-side voltage and the battery voltage is expressed as:
$$ \frac{U_{busi}}{U_{Bi}} = \frac{1}{1 – d_i} $$
where \( d_i \) is the duty cycle of the lower switch in the \( i \)-th module. The SOC of the battery module is defined as:
$$ \text{SOC}_i = \text{SOC}_o – \frac{\int I_{Bi} dt}{Q} $$
where \( \text{SOC}_o \) is the initial SOC, \( Q \) is the rated capacity of the battery module, and \( t \) is time. Substituting the previous equations, the SOC can be rewritten as:
$$ \text{SOC}_i = \text{SOC}_o – \frac{\int \frac{1}{1 – d_i} I_o dt}{Q} $$
This equation shows that the SOC of each battery module is influenced by its duty cycle. In discharge mode, a higher duty cycle results in a larger discharge current and faster SOC decrease, while in charge mode, the opposite occurs. Thus, by controlling the duty cycle, the charge and discharge currents can be regulated to achieve SOC balancing in energy storage lithium battery systems.
To address the instability in charge mode, we propose a series-type I-P droop control strategy, inspired by traditional droop control used in parallel systems. In parallel systems, droop control adjusts the output impedance to achieve current sharing, but in series-connected systems, the output current is the same for all modules. The proposed I-P droop control stabilizes power distribution by introducing a droop characteristic that relates the output current to power. The droop characteristic is designed as shown in Figure 2, where the current offset at zero voltage is set to a common point \( I_{\text{set}} \). The droop coefficients \( g_{di} \) are different for each module to allocate power effectively. After applying droop control, the bus-side current reference for the \( i \)-th module, \( I_{oi\_droop} \), is given by:
$$ I_{oi\_droop} = \begin{cases}
(1 + k_{dp}) I_{o\_ref} – g_{di} P_i, & \text{discharge mode} \\
(1 – k_{dp}) I_{o\_ref} + g_{di} P_i, & \text{charge mode}
\end{cases} $$
where \( k_{dp} \) is the cluster current compensation coefficient, \( I_{o\_ref} \) is the cluster current reference, and \( P_i \) is the power of the \( i \)-th module. The droop coefficient \( g_{di} \) is designed as:
$$ g_{di} = \frac{k_{dp} I_{o\_ref}}{P_{i\_ref}} = \frac{k_{dp}}{U_{busi\_ref}} $$
where \( P_{i\_ref} \) and \( U_{busi\_ref} \) are the power reference and bus-side voltage reference for the \( i \)-th module, respectively. To incorporate SOC balancing, a proportional balancing strategy is introduced, where the bus-side voltage reference is adjusted based on the SOC of each module:
$$ U_{busi\_ref} = \begin{cases}
\frac{U_{dc}}{N} + k_p (\text{SOC}_i – \text{SOC}_{\text{avg}}), & \text{discharge mode} \\
\frac{U_{dc}}{N} + k_p (\text{SOC}_{\text{avg}} – \text{SOC}_i), & \text{charge mode}
\end{cases} $$
where \( U_{dc} \) is the DC grid voltage, \( N \) is the number of modules, \( k_p \) is the balancing acceleration factor, and \( \text{SOC}_{\text{avg}} \) is the average SOC of the modules. Substituting this into the droop coefficient expression yields:
$$ g_{di} = \begin{cases}
\frac{k_{dp}}{\frac{U_{dc}}{N} + k_p (\text{SOC}_i – \text{SOC}_{\text{avg}})}, & \text{discharge mode} \\
\frac{k_{dp}}{\frac{U_{dc}}{N} + k_p (\text{SOC}_{\text{avg}} – \text{SOC}_i)}, & \text{charge mode}
\end{cases} $$
The battery-side current reference is then derived as:
$$ I_{Bi\_ref} = \frac{U_{busi} I_{oi\_droop}}{U_{Bi}} $$
This current reference is used to control the charge and discharge currents of each battery module in the energy storage lithium battery system. The control structure is illustrated in Figure 3, where the current regulator \( G_{pi}(s) \) generates the duty cycles for the switches.
While the proportional balancing strategy achieves SOC balancing, its speed decreases as the SOC difference between modules reduces because the voltage and current differences diminish. To enhance the balancing speed, we propose an improved balancing strategy that optimizes the voltage division coefficient. This strategy maintains the maximum allowable voltage difference between modules during the balancing process, ensuring that the charge and discharge current differences remain at their maximum values. This approach decouples power control from balancing control by keeping the sum of the voltage division coefficients constant. The voltage division coefficient \( g_{ui} \) is defined as the inverse of the droop coefficient, \( g_{ui} = g_{di}^{-1} \). The bus-side voltage for each module is expressed as:
$$ U_{busi} = \frac{g_{ui}}{\sum_{i=1}^{N} g_{ui}} U_{dc} $$
The output current \( I_o \) is given by:
$$ I_o = \frac{I_{\text{set}}}{1 – \frac{U_{dc}}{\sum_{i=1}^{N} g_{ui}}} $$
and the total system power \( P_{\text{total}} \) is:
$$ P_{\text{total}} = \frac{I_{\text{set}}}{\frac{1}{U_{dc}} – \frac{1}{\sum_{i=1}^{N} g_{ui}}} $$
By keeping the sum of \( g_{ui} \) constant, power control is achieved by adjusting \( I_{\text{set}} \), while balancing control is achieved by adjusting individual \( g_{ui} \) values. The maximum voltage division coefficient \( g_{u\_max} \) is determined based on the maximum allowable bus-side voltage \( U_{bus\_max} \):
$$ g_{u\_max} = \frac{U_{bus\_max}}{U_{dc}} \sum_{i=1}^{N} g_{ui} $$
The voltage division coefficient for each module is designed as:
$$ g_{ui} = \begin{cases}
g_{u\_max} – \frac{\text{SOC}_{\text{max}} – \text{SOC}_i}{\text{SOC}_{\text{max}} – \text{SOC}_{\text{min}}} (g_{u\_max} – g_{u\_min}), & \text{discharge mode} \\
g_{u\_max} – \frac{\text{SOC}_i – \text{SOC}_{\text{min}}}{\text{SOC}_{\text{max}} – \text{SOC}_{\text{min}}} (g_{u\_max} – g_{u\_min}), & \text{charge mode}
\end{cases} $$
where \( \text{SOC}_{\text{max}} \) and \( \text{SOC}_{\text{min}} \) are the maximum and minimum SOC values among the modules, and \( g_{u\_min} \) is the minimum voltage division coefficient, derived as:
$$ g_{u\_min} = \begin{cases}
-\frac{\text{SOC}_{\text{max}} – \text{SOC}_{\text{min}}}{N \cdot \text{SOC}_{\text{max}} – \sum_{i=1}^{N} \text{SOC}_i} (N \cdot g_{u\_max} – \sum_{i=1}^{N} g_{ui}) + g_{u\_max}, & \text{discharge mode} \\
-\frac{\text{SOC}_{\text{max}} – \text{SOC}_{\text{min}}}{\sum_{i=1}^{N} \text{SOC}_i – N \cdot \text{SOC}_{\text{min}}} (N \cdot g_{u\_max} – \sum_{i=1}^{N} g_{ui}) + g_{u\_max}, & \text{charge mode}
\end{cases} $$
The sum of the voltage division coefficients is predetermined from the power control setup. The improved balancing strategy flowchart is shown in Figure 4, and the control block diagram is depicted in Figure 5. Once the balancing index is met, the system switches to the proportional balancing strategy for fine-tuning.
To validate the proposed strategies, we conducted simulation studies on a cascaded modular energy storage lithium battery system with six battery modules. Each module consists of 32 series-connected 280 Ah lithium iron phosphate cells, with a rated voltage of 102.4 V per module. The system is connected to a 750 V DC grid. The initial SOC values of the modules are set to 44%, 46%, 48%, 50%, 52%, and 54%, with a total power of 8.4 kW. The cluster current reference is set to 20 A in discharge mode and -20 A in charge mode.
In discharge mode, the simulation results for the proportional balancing strategy are shown in Figure 7. The bus-side voltages are initially allocated proportionally to the SOC values, resulting in voltages of 105 V, 91 V, 77 V, 63 V, 55 V, and 35 V for modules 1 to 6, respectively. The module with the highest SOC (module 1) has the highest discharge current. As the SOC balances, the voltages and currents converge. The SOC difference reduces from 10% to 0.2% in 2000 seconds. However, the balancing speed slows down as the SOC difference decreases.
The improved balancing strategy maintains maximum voltage differences during discharge, as shown in Figure 8. The SOC difference reduces from 10% to 0.1% in 516.1 seconds, significantly faster than the proportional strategy. The droop coefficients for the improved strategy in discharge mode are shown in Figure 9. Initially, the module with the highest SOC has the smallest droop coefficient (\(9.524 \times 10^{-4} \text{V}^{-1}\)), while the module with the lowest SOC has the largest (\(2.9 \times 10^{-3} \text{V}^{-1}\)). Eventually, all coefficients converge to \(1.43 \times 10^{-3} \text{V}^{-1}\).
In charge mode, the proportional balancing strategy results are shown in Figure 10. The system stabilizes with SOC balancing, but the speed is slow. The improved strategy, as shown in Figure 11, achieves a reduction in SOC difference from 10% to 0.1% in 551.4 seconds. The droop coefficients in charge mode (Figure 12) show the module with the highest SOC having the largest coefficient initially (\(2.9 \times 10^{-3} \text{V}^{-1}\)) and the lowest SOC module having the smallest (\(9.524 \times 10^{-4} \text{V}^{-1}\)), converging to \(1.43 \times 10^{-3} \text{V}^{-1}\).
The balancing times for different SOC difference targets are summarized in Table 1. For a target SOC difference of 1%, the improved strategy reduces the balancing time by 60.9% in charge mode and 61.0% in discharge mode compared to the proportional strategy. For a target of 0.5%, the improvements are 68.28% and 68.26%, respectively. This demonstrates the effectiveness of the improved strategy, especially when the SOC difference is small.
| SOC Difference (%) | Discharge Mode – Proportional (s) | Discharge Mode – Improved (s) | Charge Mode – Proportional (s) | Charge Mode – Improved (s) |
|---|---|---|---|---|
| 3 | 634.21 | 366.87 | 671.35 | 389.09 |
| 2 | 846.36 | 418.67 | 897.49 | 444.93 |
| 1 | 1205.75 | 470.18 | 1282.19 | 500.89 |
| 0.5 | 1562.24 | 495.78 | 1667.37 | 528.91 |
In conclusion, this paper addresses the instability issues in grid-connected energy storage lithium battery systems during charge mode by proposing a series-type I-P droop control strategy. This approach enables stable power distribution and SOC balancing. The proportional balancing strategy based on I-P droop control achieves SOC balancing but at a slow speed when SOC differences are small. The improved balancing strategy optimizes the voltage division coefficients to maintain maximum current differences, significantly accelerating the balancing process. Simulation results confirm that both strategies achieve stable bus-side voltage, power distribution, and SOC balancing in charge and discharge modes. The improved strategy reduces balancing time by over 60% compared to the proportional strategy, making it highly suitable for practical applications in energy storage lithium battery systems. Future work will focus on real-time implementation and optimization for larger-scale systems.