In the context of advancing renewable energy technologies and the global push for carbon neutrality, energy storage systems have emerged as a critical solution to address issues like wind and solar curtailment by managing energy across time and space. Among various energy storage technologies, electrochemical storage, particularly lithium battery energy storage system (BESS), has gained significant traction due to its long lifespan and high flexibility. Lithium BESS are widely deployed in high-voltage DC applications, such as electric vehicles and microgrids, where they enhance grid stability and efficiency. However, challenges like inconsistent battery parameters and state of charge (SOC) imbalances can lead to overcharging or over-discharging, compromising system safety and longevity. This paper focuses on addressing these issues in a modular cascaded BESS topology, where battery modules are integrated with power converters to form battery power modules, connected in series to a DC grid. We propose novel control strategies to ensure stable power distribution and SOC balancing, leveraging下垂 control principles adapted for series-connected systems.
The modular cascaded BESS architecture, as illustrated in the following figure, consists of multiple battery modules, each coupled with a bidirectional DC-DC power converter. These battery power modules are connected in series at the output side to interface with a DC grid. In this setup, each module independently manages its charging and discharging currents, enabling precise control over individual battery modules. However, in grid-connected scenarios, the DC grid voltage is fixed, necessitating stable power allocation among modules. Our analysis reveals that independent current control by module controllers leads to instability in charging mode, causing current fluctuations and divergent bus-side voltages. To overcome this, we introduce a series-type I-P下垂 control strategy, inspired by parallel下垂 concepts, to achieve stable power sharing. Additionally, we develop SOC balancing strategies, including a proportional approach and an improved method with optimized voltage division coefficients, to accelerate均衡速度 while decoupling power and均衡 control. Simulation results from a six-module system validate the effectiveness of our proposals, demonstrating rapid SOC balancing and stable operation in both charging and discharging modes.
The battery energy storage system (BESS) topology under study employs a series-connected configuration of battery power modules. Each module comprises a battery pack, formed by series-connected lithium-ion cells, and a bidirectional DC-DC converter, such as a two-phase interleaved buck-boost converter. The output sides of these modules are connected in series, forming a string that interfaces with a DC grid. Key parameters include module voltages, bus-side voltages, and currents. For instance, the bus-side voltage $U_{busi}$ and current $I_{busi}$ for the $i$-th module relate to the battery voltage $U_{Bi}$ and current $I_{Bi}$ through power conservation, neglecting losses:
$$ I_{Bi} = \frac{U_{busi} I_{busi}}{U_{Bi}} $$
In discharging mode, the DC-DC converter operates in boost mode, and the relationship between bus-side and battery voltages is given by:
$$ \frac{U_{busi}}{U_{Bi}} = \frac{1}{1 – d_i} $$
where $d_i$ is the duty cycle of the lower switch in the converter. The SOC of each battery module, denoted as $SOC_i$, evolves over time based on the charging or discharging current:
$$ SOC_i = SOC_{i0} – \frac{\int I_{Bi} dt}{Q} $$
where $SOC_{i0}$ is the initial SOC, $Q$ is the rated capacity of the battery module, and $t$ is time. Substituting the previous equations, we derive:
$$ SOC_i = SOC_{i0} – \frac{\int \frac{1}{1 – d_i} I_o dt}{Q} $$
This indicates that the SOC change rate depends on the duty cycle, allowing control over current distribution to achieve SOC balancing. In discharging mode, a higher SOC module should have a larger bus-side voltage and duty cycle to discharge faster, while in charging mode, the opposite applies. Thus, by regulating duty cycles, we can均衡 the SOC across modules.
To address the instability in charging mode, we propose a series-type I-P下垂 control strategy. Traditional下垂 control is commonly used in parallel-connected systems to achieve current sharing by adjusting output impedances. For series-connected BESS, we adapt this concept to stabilize power distribution. The I-P下垂 characteristic relates the output current $I_o$ to the power $P_i$ of each module, with a下垂 coefficient $g_{di}$. The下垂 curve is designed such that different modules have distinct下垂 coefficients, intersecting a reference current line $I_{set}$ to allocate power. The bus-side current reference after下垂 control, $I_{oi\_droop}$, is computed as:
$$ I_{oi\_droop} = \begin{cases}
(1 + k_{dp}) I_{o\_ref} – g_{di} P_i & \text{for discharging mode} \\
(1 – k_{dp}) I_{o\_ref} + g_{di} P_i & \text{for charging mode}
\end{cases} $$
where $k_{dp}$ is a compensation factor for current offset, and $I_{o\_ref}$ is the reference cluster current. The下垂 coefficient $g_{di}$ is designed based on the bus-side voltage reference $U_{busi\_ref}$:
$$ g_{di} = \frac{k_{dp}}{U_{busi\_ref}} $$
For SOC balancing, we first introduce a proportional均衡 strategy, where the bus-side voltage reference is adjusted according to the SOC deviation from the average:
$$ U_{busi\_ref} = \begin{cases}
\frac{U_{dc}}{N} + k_p (SOC_i – SOC_{avg}) & \text{for discharging mode} \\
\frac{U_{dc}}{N} + k_p (SOC_{avg} – SOC_i) & \text{for charging mode}
\end{cases} $$
where $U_{dc}$ is the DC grid voltage, $N$ is the number of modules, $k_p$ is an acceleration factor, and $SOC_{avg}$ is the average SOC. Substituting into the下垂 coefficient expression, we get:
$$ g_{di} = \begin{cases}
\frac{k_{dp}}{\frac{U_{dc}}{N} + k_p (SOC_i – SOC_{avg})} & \text{for discharging mode} \\
\frac{k_{dp}}{\frac{U_{dc}}{N} + k_p (SOC_{avg} – SOC_i)} & \text{for charging mode}
\end{cases} $$
The battery-side current reference $I_{Bi\_ref}$ is then derived from power balance:
$$ I_{Bi\_ref} = \frac{U_{busi} I_{oi\_droop}}{U_{Bi}} $$
This proportional strategy ensures that modules with higher SOC discharge more or charge less, promoting均衡. However, as SOC differences diminish, the voltage and current differences decrease, slowing down the均衡 process. To enhance均衡 speed, we propose an improved均衡 strategy that maintains maximum voltage differences during均衡. We define a voltage division coefficient $g_{ui} = g_{di}^{-1}$, and the bus-side voltage is allocated as:
$$ U_{busi} = \frac{g_{ui}}{\sum_{i=1}^{N} g_{ui}} U_{dc} $$
The output current $I_o$ and total power $P_{total}$ are given by:
$$ I_o = \frac{I_{set}}{1 – \frac{U_{dc}}{\sum_{i=1}^{N} g_{ui}}} $$
$$ P_{total} = I_{set} \left( \frac{1}{U_{dc}} – \frac{1}{\sum_{i=1}^{N} g_{ui}} \right) $$
By keeping the sum of $g_{ui}$ constant, we decouple power control (via $I_{set}$) from均衡 control (via $g_{ui}$). For均衡, we set the maximum and minimum $g_{ui}$ values based on SOC extremes. For example, in discharging mode, the module with the highest SOC gets $g_{ui} = g_{u\_max}$, and the lowest gets $g_{ui} = g_{u\_min}$, with linear interpolation for others:
$$ g_{ui} = \begin{cases}
g_{u\_max} – \frac{SOC_{max} – SOC_i}{SOC_{max} – SOC_{min}} (g_{u\_max} – g_{u\_min}) & \text{for discharging mode} \\
g_{u\_max} – \frac{SOC_i – SOC_{min}}{SOC_{max} – SOC_{min}} (g_{u\_max} – g_{u\_min}) & \text{for charging mode}
\end{cases} $$
The minimum $g_{ui}$ is computed to maintain the sum constant. This approach ensures that current differences remain large, accelerating均衡. Once a predefined均衡 threshold is reached, we switch to the proportional strategy for fine-tuning.
We conducted simulations using a BESS with six battery modules, each with a rated voltage of 25 V and capacity of 80 Ah, connected to a 420 V DC grid. The initial SOC values were set with a 10% spread. In discharging mode, with a cluster current reference of 20 A, the proportional strategy achieved SOC均衡 but took significant time due to reducing current differences. The improved strategy maintained larger voltage and current differences, reducing均衡 time substantially. Similarly, in charging mode with a -20 A reference, the improved strategy outperformed the proportional approach. The following tables summarize the均衡 times for different SOC difference thresholds.
| SOC Difference (%) | Proportional Strategy (s) | Improved Strategy (s) |
|---|---|---|
| 3 | 634.21 | 366.87 |
| 2 | 846.36 | 418.67 |
| 1 | 1205.75 | 470.18 |
| 0.5 | 1562.24 | 495.78 |
| SOC Difference (%) | Proportional Strategy (s) | Improved Strategy (s) |
|---|---|---|
| 3 | 671.35 | 389.09 |
| 2 | 897.49 | 444.93 |
| 1 | 1282.19 | 500.89 |
| 0.5 | 1667.37 | 528.91 |
The下垂 coefficients for the improved strategy in both modes converge to a common value as均衡 is achieved, illustrating the stability of the approach. For instance, in discharging mode, the initial下垂 coefficients range from $9.524 \times 10^{-4}$ to $2.9 \times 10^{-3}$ V^{-1}, settling to $1.43 \times 10^{-3}$ V^{-1}. Similarly, in charging mode, they evolve oppositely but reach the same steady state.
In conclusion, our proposed series-type I-P下垂 control effectively stabilizes power distribution in a modular cascaded BESS, addressing the instability issues in charging mode. The integration of SOC balancing strategies, particularly the improved method with optimized voltage division, significantly accelerates均衡 while decoupling control loops. This enhances the overall performance and reliability of lithium battery energy storage systems in grid-connected applications, contributing to safer and more efficient energy management. Future work could explore real-time adaptation of control parameters and scalability to larger systems.