In recent years, the rapid integration of renewable energy sources has intensified the imbalance between generation, grid, and load, driving the exponential growth of battery energy storage system (BESS) installations. High-voltage transformerless BESS topologies, which connect directly to medium- or high-voltage grids without transformers, have emerged as a key solution for large-scale energy storage. These systems utilize cascaded H-bridge converters to manage individual battery clusters, enhancing the granularity of battery system control and overcoming the limitations posed by parameter variations among massive battery cells. This approach significantly improves system capacity, efficiency, and safety, making it suitable for hundred-megawatt-level energy storage requirements. However, the state of charge (SOC) imbalance among battery clusters can reduce the capacity utilization of the system and lead to battery abuse at the end of charging or discharging cycles. Traditional SOC balancing methods often employ fixed balancing coefficients, which may result in slow convergence or risks of over-modulation and excessive battery current rates. To address these issues, this paper proposes an adaptive fast SOC balancing control strategy that dynamically adjusts inter-phase and intra-phase balancing coefficients based on system operating conditions, ensuring rapid SOC convergence while adhering to safety constraints.
The high-voltage transformerless battery energy storage system consists of multiple cascaded power modules per phase, each comprising an H-bridge converter, a DC-link capacitor, and a battery cluster. The system is connected to the grid via filtering inductors, and the battery clusters are dispersed across the DC sides of the H-bridge converters. This structure eliminates parallel battery cluster circulation losses and enables independent control of each cluster. The SOC balancing control is divided into inter-phase SOC balancing and intra-phase SOC balancing. Inter-phase balancing is achieved by injecting a zero-sequence voltage that redistributes active power among the three phases, while intra-phase balancing modifies the modulation voltages of individual submodules based on SOC errors using carrier phase shift (CPS) modulation. The key challenge is to determine the optimal balancing coefficients that maximize the convergence speed without violating battery current limits or causing over-modulation.
For intra-phase SOC balancing, the battery cluster current after applying balancing control can be expressed as:
$$I_{kj} = \frac{P}{3NE_{\text{bat}}} + \frac{K_k I_m}{2E_{\text{bat}}} \Delta S_{\text{SOC}kj}$$
where \(P\) is the system power, \(N\) is the number of submodules per phase, \(E_{\text{bat}}\) is the battery cluster voltage, \(K_k\) is the intra-phase balancing coefficient for phase \(k\), \(I_m\) is the phase current amplitude, and \(\Delta S_{\text{SOC}kj}\) is the SOC error of the \(j\)-th submodule in phase \(k\). The optimal intra-phase balancing coefficient \(K_k\) is derived by considering the charging and discharging current boundaries and the modulation ratio limits. The maximum allowable \(K_k\) to avoid exceeding the battery current rating \(I_{\text{rated}}\) is given by:
$$K_{k1} = \frac{2(E_{\text{bat}} I_{\text{avg}} – U_m I_m \cos \phi)}{I_m (S_{\text{SOC}k,\text{min}} – S_{\text{SOC}k})}$$
$$K_{k2} = \frac{2(E_{\text{bat}} I_{\text{avg}} + U_m I_m \cos \phi)}{I_m (S_{\text{SOC}k} – S_{\text{SOC}k,\text{max}})}$$
where \(U_m\) is the peak modulation voltage per submodule, \(\phi\) is the power factor angle, and \(S_{\text{SOC}k,\text{min}}\) and \(S_{\text{SOC}k,\text{max}}\) are the minimum and maximum SOC values in phase \(k\). Similarly, the modulation ratio constraint leads to:
$$K_{k3} = \frac{\sqrt{U_C^2 – U_{\text{avg}}^2 \sin^2 \phi} – U_{\text{avg}} \cos \phi}{S_{\text{SOC}k} – S_{\text{SOC}k,\text{min}}}$$
$$K_{k4} = \frac{\sqrt{U_C^2 – U_{\text{avg}}^2 \sin^2 \phi} + U_{\text{avg}} \cos \phi}{S_{\text{SOC}k,\text{max}} – S_{\text{SOC}k}}$$
where \(U_C\) is the DC-link capacitor voltage and \(U_{\text{avg}}\) is the average modulation voltage. The optimal intra-phase balancing coefficient is then selected as:
$$K_k = \min(K_{k1}, K_{k2}, K_{k3}, K_{k4})$$
This coefficient adapts to variations in power factor, phase current amplitude, battery voltage, and SOC distribution, ensuring the fastest possible intra-phase SOC balancing without violating constraints.
For inter-phase SOC balancing, a zero-sequence voltage \(u_0 = U_0 \cos(\omega t + \theta_0)\) is injected, where \(U_0\) and \(\theta_0\) are determined based on the SOC imbalances among phases. The power adjustment per phase due to zero-sequence injection is:
$$\Delta P_k = \frac{1}{2} U_0 I_s \cos(\theta_0 – \theta_k) = K_0 P_{\text{nom}} \Delta S_{\text{SOC}k}$$
where \(K_0\) is the inter-phase balancing coefficient, \(P_{\text{nom}}\) is the nominal system power, and \(\Delta S_{\text{SOC}k}\) is the SOC error of phase \(k\). The optimal \(K_0\) is derived by considering the current and modulation constraints across phases. The current boundary conditions yield:
$$K_{01} = \frac{2(N E_{\text{bat}} I_{\text{avg}} – U_s I_m \cos \phi)}{P_{\text{nom}} (S_{\text{SOC},\text{min}} – S_{\text{SOC}})}$$
$$K_{02} = \frac{2(N E_{\text{bat}} I_{\text{avg}} + U_s I_m \cos \phi)}{P_{\text{nom}} (S_{\text{SOC}} – S_{\text{SOC},\text{max}})}$$
where \(U_s\) is the peak phase voltage. The modulation constraint is addressed by solving for the maximum \(K_0\) that ensures the modulation index of any phase does not exceed unity. The final inter-phase balancing coefficient is:
$$K_0 = \min(K_{01}, K_{02}, K_{03})$$
where \(K_{03}\) is derived from the modulation limit analysis.
To decouple the inter-phase and intra-phase balancing controls, an adaptive allocation strategy is proposed. The intra-phase unbalance degree is defined as:
$$\Theta_k = \sqrt{\frac{1}{N} \sum_{j=1}^{N} (S_{\text{SOC}kj} – S_{\text{SOC}k})^2}$$
and the inter-phase unbalance degree is \(\Delta S_{\text{SOC}} = \sqrt{\sum_{k=a,b,c} \Delta S_{\text{SOC}k}^2}\). The ratio \(\xi = (\Theta_a + \Theta_b + \Theta_c) / \Delta S_{\text{SOC}}\) indicates the relative severity of intra-phase versus inter-phase unbalance. The inter-phase balancing effort coefficient \(K_\xi\) is defined as:
$$K_\xi = \begin{cases}
0.5 \cdot (2 – \xi) & \text{if } \xi < 1 \\
0.5 / \xi & \text{if } \xi \geq 1
\end{cases}$$
The amplitude of the zero-sequence voltage is then adjusted as:
$$U_0 = \frac{2 K_\xi K_0 P_{\text{nom}} \Delta S_{\text{SOC}}}{\sqrt{3} I_s}$$
This approach ensures that the balancing capability is allocated optimally between inter-phase and intra-phase balancing based on the real-time SOC distribution.
| Parameter | Value |
|---|---|
| Grid Line Voltage (kV) | 10 |
| Rated Power (MW) | 5 |
| Rated Capacity (MWh) | 5 |
| Battery Cluster Voltage (V) | 768 |
| Submodules per Phase | 16 |
| Grid-Side Filter Inductance (mH) | 6 |
| Control Frequency (kHz) | 10 |
| DC-Side Filter Inductance (mH) | 2.5 |
| DC-Link Capacitance (mF) | 7.2 |
The proposed adaptive fast SOC balancing control for the battery energy storage system was validated through simulations in MATLAB/Simulink. A 10 kV / 5 MW / 5 MWh high-voltage transformerless BESS model was used, with parameters listed in Table 1. The simulations considered various initial SOC distributions and operating conditions to demonstrate the effectiveness of the adaptive balancing coefficients.
In the first scenario, the intra-phase SOC error was uniformly distributed within phase A. The system was charged at rated power (5 MW) for 2 seconds, followed by a reduction to 2.5 MW. The results showed that with the adaptive intra-phase balancing coefficient \(K_a\), the SOC of the lowest-SOC cluster increased rapidly while its current reached the charging boundary (160 A). After the power reduction, the modulation index of the lowest-SOC submodule reached unity, and \(K_a\) was limited by the modulation constraint. The SOC unbalance converged quickly, validating the adaptive coefficient calculation.
In the second scenario, one battery cluster in phase B had a higher initial SOC than others. During rated power charging, the highest-SOC cluster discharged at the current boundary, while other clusters charged. The adaptive coefficient \(K_b\) ensured fast SOC convergence without exceeding the discharge current limit. When the system operated at pure reactive power (5 MVA), the balancing speed increased due to the higher allowable coefficient under low power factor conditions.
In the third scenario, one cluster in phase C had a lower initial SOC. The adaptive coefficient \(K_c\) allowed the lowest-SOC cluster to charge at the current boundary, accelerating SOC balancing. The simulation results confirmed that the balancing coefficients adapt to changes in power, power factor, and SOC distribution, maximizing the balancing speed while maintaining safe operation.
Finally, the combined inter-phase and intra-phase balancing control was tested. The system started with both inter-phase and intra-phase SOC unbalances. The adaptive effort coefficient \(K_\xi\) initially prioritized intra-phase balancing, as the intra-phase unbalance was more severe. After intra-phase convergence, the inter-phase balancing intensified, and the system achieved full SOC equilibrium within 5 seconds. The zero-sequence voltage injection was constrained by the modulation limit, and the adaptive control ensured no over-modulation or over-current events.
| Condition | Balancing Coefficient | Convergence Time (s) | Limiting Factor |
|---|---|---|---|
| 5 MW Charging, Uniform SOC Error | \(K_a = K_{a1}\) | 2.0 | Charging Current |
| 2.5 MW Charging, Uniform SOC Error | \(K_a = K_{a3}\) | 1.5 | Modulation Index |
| 5 MVA Reactive, Uniform SOC Error | \(K_a = K_{a4}\) | 1.0 | Modulation Index |
| 5 MW Charging, Single High SOC | \(K_b = K_{b2}\) | 2.2 | Discharging Current |
| 2.5 MW Charging, Single High SOC | \(K_b = K_{b4}\) | 1.8 | Modulation Index |
| 5 MVA Reactive, Single High SOC | \(K_b = K_{b4}\) | 1.3 | Modulation Index |
| 5 MW Charging, Single Low SOC | \(K_c = K_{c1}\) | 2.1 | Charging Current |
| 2.5 MW Charging, Single Low SOC | \(K_c = K_{c3}\) | 1.7 | Modulation Index |
| 5 MVA Reactive, Single Low SOC | \(K_c = K_{c3}\) | 1.2 | Modulation Index |
| Combined Inter/Intra-Phase Balancing | \(K_0 = K_{03}\), \(K_\xi\) adaptive | 5.0 | Modulation Index |
The proposed adaptive fast SOC balancing control for high-voltage transformerless battery energy storage systems effectively addresses the trade-off between balancing speed and safety constraints. By deriving optimal intra-phase and inter-phase balancing coefficients that adapt to power factor, phase current, battery voltage, and SOC distribution, the system achieves the fastest possible SOC convergence without over-modulation or excessive battery currents. The adaptive decoupling control allocates balancing effort based on the relative severity of inter-phase and intra-phase unbalances, ensuring comprehensive SOC equilibrium across all battery clusters. Simulation results on a 10 kV/5 MW/5 MWh BESS model validate the theoretical analysis and demonstrate the strategy’s effectiveness under various operating conditions. This approach enhances the capacity utilization and longevity of battery energy storage systems, supporting the reliable integration of renewable energy sources.
The battery energy storage system topology and control strategy presented here offer a scalable solution for large-scale energy storage applications. Future work could explore the integration of this balancing control with fault tolerance mechanisms and real-time optimization algorithms to further improve the performance and reliability of battery energy storage systems in dynamic grid environments.