In modern DC microgrids, the integration of renewable energy sources such as wind and photovoltaic power into distributed generation systems has become widespread. Within these systems, the battery energy storage system plays a pivotal role as an energy storage unit, ensuring grid stability and reliability. The bidirectional DC-DC converter serves as a critical link between the generation system and the battery energy storage system, facilitating bidirectional energy flow to balance power demands caused by fluctuations in distributed sources and loads. Therefore, optimizing control strategies for these converters to enhance system stability and responsiveness is a key research focus. Multi-phase interleaved parallel bidirectional DC-DC converters are particularly favored in applications between the DC bus and battery energy storage systems due to their advantages of low switch current stress, reduced switching losses, and high power density. However, inconsistencies in parasitic parameters among parallel modules can lead to unequal current sharing among phases, potentially causing device failure and system malfunction. Hence, developing a control strategy that ensures balanced current sharing, high reliability, fast response, and adaptability to high-current scenarios is essential for advancing battery energy storage system technology.
This article addresses the current imbalance issue in three-phase interleaved parallel bidirectional Buck-Boost converters by proposing a novel current sharing method based on Sliding Mode Control and Model Predictive Control (SMC-MPC). The voltage outer loop employs sliding mode control to derive the reference inductor current expression, enhancing system robustness and response speed. The current inner loop utilizes model predictive control, where the discrete state-space equations are established, an evaluation function is constructed, and the optimal duty cycle expressions are derived theoretically. Duty cycle compensation is then applied to achieve balanced current sharing among phases. The effectiveness of this strategy is validated through simulations in Matlab/Simulink and experimental tests on a 500 W prototype. Results demonstrate significant improvements in reducing overshoot, enhancing current sharing accuracy, and boosting robustness compared to traditional PI-MPC strategies, confirming the feasibility and superiority of the proposed approach for battery energy storage system applications.
The topology of the three-phase interleaved parallel bidirectional Buck-Boost converter is fundamental to its operation. It consists of three identical Buck-Boost circuits connected in parallel, enabling bidirectional energy transfer. In Boost mode, energy flows from the input to the output, with switches S1, S3, and S5 controlled via phase-shifted signals to produce interleaved currents. Conversely, in Buck mode, energy flows from the output to the input, with switches S2, S4, and S6 active. The interleaving technique triples the effective switching frequency, reducing input and output current ripples and improving power density. However, parasitic resistances in inductors and switches can cause current imbalances, necessitating precise control. The converter operates in Continuous Conduction Mode (CCM) across various duty cycles, and its behavior can be modeled using state-space averaging. For a single-phase Buck-Boost converter in Boost mode, the continuous state-space equations are:
$$
\frac{d}{dt} \begin{bmatrix} i_L \\ U_o \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 0 & -\frac{1}{RC} \end{bmatrix} \begin{bmatrix} i_L \\ U_o \end{bmatrix} + \begin{bmatrix} \frac{1}{L} \\ 0 \end{bmatrix} U_{in} \quad \text{(switch ON)}
$$
$$
\frac{d}{dt} \begin{bmatrix} i_L \\ U_o \end{bmatrix} = \begin{bmatrix} 0 & -\frac{1}{L} \\ \frac{1}{C} & -\frac{1}{RC} \end{bmatrix} \begin{bmatrix} i_L \\ U_o \end{bmatrix} + \begin{bmatrix} \frac{1}{L} \\ 0 \end{bmatrix} U_{in} \quad \text{(switch OFF)}
$$
Discretizing these equations yields the discrete state-space model, which is crucial for digital control implementation. For Boost mode, the discrete equations at the (k+1)-th sampling period are:
$$
i_L(k+1) = i_L(k) + \frac{T_s}{L} \left[ U_{in}(k) – (1 – D_{\text{Boost}}(k)) U_o(k) \right]
$$
$$
U_o(k+1) = U_o(k) + \frac{T_s}{C} \left[ (1 – D_{\text{Boost}}(k)) i_L(k) – \frac{U_o(k)}{R} \right]
$$
where \( T_s \) is the sampling period, \( D_{\text{Boost}}(k) \) is the duty cycle in Boost mode, \( i_L(k) \) is the inductor current, \( U_{in}(k) \) is the input voltage, \( U_o(k) \) is the output voltage, and \( R \) is the load resistance. Similar equations can be derived for Buck mode. The current and voltage ripples under full duty cycle ranges for both modes are summarized in Table 1, highlighting the benefits of interleaving in reducing ripple magnitudes.
| Mode | Duty Cycle Range | Input Current Ripple (Boost) / Output Current Ripple (Buck) | Output Voltage Ripple (Boost) / Input Voltage Ripple (Buck) |
|---|---|---|---|
| Boost | \( 0 < D_{\text{Boost}} < \frac{1}{3} \) | \( \Delta i_{in} = \frac{U_o D_{\text{Boost}} (1 – 3D_{\text{Boost}}) T_s}{L} \) | \( \Delta U_{C2} = \frac{U_o D_{\text{Boost}} (1 – 3D_{\text{Boost}}) T_s}{3RC(1 – D_{\text{Boost}})} \) |
| \( \frac{1}{3} \leq D_{\text{Boost}} \leq \frac{2}{3} \) | \( \Delta i_{in} = \frac{U_o T_s (3D_{\text{Boost}} – 1)(2 – 3D_{\text{Boost}})}{3L} \) | \( \Delta U_{C2} = \frac{U_o T_s (3D_{\text{Boost}} – 1)(2 – 3D_{\text{Boost}})}{9RC(1 – D_{\text{Boost}})} \) | |
| \( \frac{2}{3} < D_{\text{Boost}} \leq 1 \) | \( \Delta i_{in} = \frac{U_o T_s (1 – D_{\text{Boost}})(3D_{\text{Boost}} – 2)}{L} \) | \( \Delta U_{C2} = \frac{U_o T_s (3D_{\text{Boost}} – 2)}{3RC} \) | |
| Buck | \( 0 < D_{\text{Buck}} < \frac{1}{3} \) | \( \Delta i_o = \frac{U_o D_{\text{Buck}} (1 – 3D_{\text{Buck}}) T_s}{L} \) | \( \Delta U_{C1} = \frac{U_{in} T_s^2 (1 – 3D_{\text{Buck}})^2}{24C_1 L} \) |
| \( \frac{1}{3} \leq D_{\text{Buck}} \leq \frac{2}{3} \) | \( \Delta i_o = \frac{U_o T_s (3D_{\text{Buck}} – 1)(2 – 3D_{\text{Buck}})}{3L} \) | \( \Delta U_{C1} = \frac{U_{in} T_s^2 (3D_{\text{Buck}} – 1)(2 – 3D_{\text{Buck}})}{36C_1 L D_{\text{Buck}}} \) | |
| \( \frac{2}{3} < D_{\text{Buck}} \leq 1 \) | \( \Delta i_o = \frac{U_o T_s (1 – D_{\text{Buck}})(3D_{\text{Buck}} – 2)}{L} \) | \( \Delta U_{C1} = \frac{U_{in} T_s^2 (1 – D_{\text{Buck}})(3D_{\text{Buck}} – 2)}{24C_1 L D_{\text{Buck}}} \) |
The proposed SMC-MPC strategy is designed to overcome current imbalances caused by parasitic parameter variations. The control structure consists of a voltage outer loop with sliding mode control and a current inner loop with model predictive control. This combination leverages the robustness of sliding mode control against disturbances and the precision of predictive control for fast dynamic response. In the voltage outer loop, the sliding surface is defined using state variables that include the inductor current error, output voltage error, and integral of the output voltage error. This design ensures zero steady-state error and enhances system stability. The sliding surface \( S \) is given by:
$$
S = \Delta_1 \sum_{m=1}^{3} (i_{L_m,\text{ref}} – i_{L_m}) + \Delta_2 (U_{o,\text{ref}} – U_o) + \Delta_3 \int (U_{o,\text{ref}} – U_o) dt
$$
where \( \Delta_1, \Delta_2, \Delta_3 \) are positive sliding coefficients, \( i_{L_m,\text{ref}} \) is the reference inductor current for phase m, \( i_{L_m} \) is the actual inductor current, \( U_{o,\text{ref}} \) is the reference output voltage, and \( U_o \) is the actual output voltage. By setting \( S = 0 \) and solving for the reference inductor current, we obtain:
$$
i_{L,\text{ref}} = \frac{1}{\Delta_1} \left[ \sum_{m=1}^{3} i_{L_m} – \Delta_2 (U_{o,\text{ref}} – U_o) – \Delta_3 \int (U_{o,\text{ref}} – U_o) dt \right]
$$
This reference current is then fed to the current inner loop. The model predictive control in the inner loop minimizes an evaluation function to compute the optimal duty cycle for each phase. The evaluation function \( Q \) is defined as:
$$
Q = [U_o(k+1) – U_{o,\text{ref}}]^2 + [i_L(k+1) – i_{L,\text{ref}}]^2
$$
Substituting the discrete state-space equations into \( Q \) and minimizing it with respect to the duty cycle yields the optimal duty cycle expressions. For Boost mode, the optimal duty cycle for phase a is derived as:
$$
D_{\text{Boost1}}(k) = 1 – \frac{L_1 C_2 U_o(k) – L_1 C_2 U_{o,\text{ref}} + T_s U_{in}(k) C_2}{T_s U_o(k) C_2 + \frac{T_s U_o(k) C_2^2 L_1 i_{L1}(k)}{C_2 U_o(k) T_s}}
$$
After simplification and considering load current \( i_o(k) = U_o(k)/R \), the expression becomes:
$$
D_{\text{Boost1}}(k) = 1 + \frac{C_2 L_1 [i_{L1}(k) – i_{L1,\text{ref}}]}{T_s C_2 U_o(k)} – \frac{T_s [U_{in}(k) – U_o(k)]}{C_2 U_o(k) T_s}
$$
Similarly, for phases b and c, the duty cycles are:
$$
D_{\text{Boost2}}(k) = 1 + \frac{C_2 L_2 [i_{L2}(k) – i_{L2,\text{ref}}]}{T_s C_2 U_o(k)} – \frac{T_s [U_{in}(k) – U_o(k)]}{C_2 U_o(k) T_s}
$$
$$
D_{\text{Boost3}}(k) = 1 + \frac{C_2 L_3 [i_{L3}(k) – i_{L3,\text{ref}}]}{T_s C_2 U_o(k)} – \frac{T_s [U_{in}(k) – U_o(k)]}{C_2 U_o(k) T_s}
$$
For Buck mode, the optimal duty cycle for phase a is:
$$
D_{\text{Buck1}}(k) = \frac{L_1 i_{L1,\text{ref}} – L_1 i_{L1}(k) + T_s U_{in}(k)}{T_s U_o(k)}
$$
And for phases b and c:
$$
D_{\text{Buck2}}(k) = \frac{L_2 i_{L2,\text{ref}} – L_2 i_{L2}(k) + T_s U_{in}(k)}{T_s U_o(k)}
$$
$$
D_{\text{Buck3}}(k) = \frac{L_3 i_{L3,\text{ref}} – L_3 i_{L3}(k) + T_s U_{in}(k)}{T_s U_o(k)}
$$
These duty cycles are adjusted in real-time to compensate for parasitic mismatches, ensuring balanced current sharing. The overall control scheme incorporates a maximum current sharing module that monitors phase currents and provides correction signals to the reference current, enhancing robustness during transients.
To validate the SMC-MPC strategy, simulation studies were conducted in Matlab/Simulink under various operating conditions. The converter parameters are listed in Table 2, which are typical for a battery energy storage system interface. The simulations compared the proposed SMC-MPC with the traditional PI-MPC strategy in terms of current sharing accuracy, dynamic response, and robustness.
| Parameter | Value |
|---|---|
| Input Voltage \( U_{in} \) | 10 V to 40 V |
| Output Voltage \( U_o \) | 50 V |
| Inductance \( L_1 \) | 0.82 mH |
| Parasitic Resistance of \( L_1 \) | 0.08 Ω |
| Inductance \( L_2 \) | 0.80 mH |
| Parasitic Resistance of \( L_2 \) | 0.10 Ω |
| Inductance \( L_3 \) | 0.78 mH |
| Parasitic Resistance of \( L_3 \) | 0.12 Ω |
| Filter Capacitance \( C \) | 470 μF |
| Switching Frequency \( f_s \) | 20 kHz |
| Sampling Frequency | 20 kHz |
| Control Step Size | 0.05 s |
| PI Parameters (for comparison) | \( K_p = 0.1 \), \( K_i = 20 \) |
In Boost mode with a duty cycle of 0.5, the SMC-MPC strategy reduced the current sharing error to 1.98% compared to 2.37% with PI-MPC. The overshoot was eliminated, and the settling time improved from 15 ms to 5 ms. In Buck mode with the same duty cycle, the current sharing error dropped to 2.69% from 3.56%, with settling time reduced from 13 ms to 5 ms and overshoot eliminated. These results are summarized in Table 3, demonstrating the superior performance of SMC-MPC in both steady-state and transient conditions for battery energy storage system applications.
| Control Method | Operating Mode | Overshoot (%) | Settling Time (ms) | Current Sharing Error (%) |
|---|---|---|---|---|
| PI-MPC | Buck | 32.8 | 13 | 3.56 |
| Boost | 30.3 | 15 | 2.37 | |
| SMC-MPC | Buck | 0 | 5 | 2.69 |
| Boost | 0 | 5 | 1.98 |
Dynamic performance was evaluated under load step changes. In Boost mode, the load was switched between 10 Ω and 20 Ω, while in Buck mode, it varied between 0.4 Ω and 0.8 Ω. The SMC-MPC strategy maintained balanced currents with fast recovery, showcasing its robustness. For instance, in Buck mode, the output current stabilized within 0.4 ms without overshoot, whereas PI-MPC exhibited 11.5% overshoot and a 50 ms settling time. This highlights the effectiveness of SMC-MPC in handling disturbances common in battery energy storage systems, where load fluctuations can occur due to varying energy demands.
Experimental verification was carried out on a 500 W prototype, as shown in the earlier figure. The prototype used MOSFETs (IRF3205PBF) and a TMS320F28335 DSP for control. Current sensing was achieved via Hall effect sensors. Tests were conducted in both Boost and Buck modes at different duty cycles. The experimental results aligned with simulations, confirming the practicality of the SMC-MPC strategy. In Boost mode at duty cycle 0.3, the current sharing error was 2% with SMC-MPC versus 4% with PI-MPC. In Buck mode at duty cycle 0.7, the error was 1% with SMC-MPC compared to 4% with PI-MPC. Tables 4 and 5 detail the experimental current sharing errors for both modes, emphasizing the consistency of the proposed method.
| Control Strategy | Phase | Average Inductor Current (A) | Current Sharing Error (%) |
|---|---|---|---|
| PI-MPC | a | 2.45 | 4 |
| b | 2.09 | ||
| c | 2.41 | ||
| SMC-MPC | a | 2.32 | 2 |
| b | 2.35 | ||
| c | 2.29 |
| Control Strategy | Phase | Average Inductor Current (A) | Current Sharing Error (%) |
|---|---|---|---|
| PI-MPC | a | 5.12 | 4 |
| b | 4.96 | ||
| c | 4.98 | ||
| SMC-MPC | a | 4.95 | 1 |
| b | 4.92 | ||
| c | 4.86 |
The mathematical robustness of the SMC-MPC strategy stems from its combination of sliding mode control and model predictive control. Sliding mode control ensures system trajectories reach and stay on the sliding surface despite uncertainties, making it ideal for handling parameter variations in battery energy storage systems. The sliding surface design incorporates integral action to eliminate steady-state errors, which is critical for maintaining voltage regulation in DC microgrids. The sliding coefficients \( \Delta_1, \Delta_2, \Delta_3 \) are chosen based on system dynamics, typically through trial and error or optimization techniques like pole placement. For instance, selecting \( \Delta_1 = 1 \), \( \Delta_2 = 0.5 \), and \( \Delta_3 = 0.1 \) can provide a balance between response speed and stability. The model predictive control, on the other hand, optimizes future behavior based on a discrete model, allowing precise current tracking. The evaluation function \( Q \) can be extended to include weighting factors for multi-objective optimization, such as:
$$
Q = \alpha [U_o(k+1) – U_{o,\text{ref}}]^2 + \beta [i_L(k+1) – i_{L,\text{ref}}]^2
$$
where \( \alpha \) and \( \beta \) are tuning parameters that prioritize voltage or current tracking. In our implementation, \( \alpha = \beta = 1 \) for equal emphasis. The derivation of duty cycle expressions involves solving \( \partial Q / \partial D = 0 \), which yields analytical solutions that are computationally efficient for real-time DSP implementation. This efficiency is vital for battery energy storage systems, where fast control loops are needed to manage rapid energy exchanges.
Furthermore, the SMC-MPC strategy enhances the reliability of the battery energy storage system by reducing thermal stress on components. Balanced current sharing ensures that no single phase overheats, prolonging the lifespan of inductors and switches. This is particularly important in high-power applications, where uneven current distribution can lead to premature failure. The strategy also improves overall system efficiency by minimizing circulating currents and losses associated with current imbalances. In terms of scalability, the control method can be extended to n-phase interleaved converters by modifying the sliding surface and evaluation function to include additional phases. For example, for an n-phase system, the sliding surface becomes:
$$
S = \Delta_1 \sum_{m=1}^{n} (i_{L_m,\text{ref}} – i_{L_m}) + \Delta_2 (U_{o,\text{ref}} – U_o) + \Delta_3 \int (U_{o,\text{ref}} – U_o) dt
$$
and the evaluation function includes terms for all phases. This flexibility makes SMC-MPC suitable for large-scale battery energy storage systems with multiple parallel converters.
In comparison to other current sharing methods, such as master-slave or droop control, SMC-MPC offers superior dynamic performance and accuracy. Master-slave methods rely on communication between modules, which can introduce delays and single-point failures. Droop control, while decentralized, often sacrifices voltage regulation for current sharing. SMC-MPC, being a combined approach, achieves both objectives without external communication, leveraging local measurements only. This autonomy is advantageous in distributed battery energy storage systems, where reliability and simplicity are paramount. Additionally, the use of predictive control reduces the need for extensive parameter tuning, as the controller inherently adapts to system changes through the discrete model. This adaptivity is crucial in battery energy storage systems, where parameters like battery internal resistance can vary with state of charge and temperature.
To further illustrate the benefits, consider the impact of the SMC-MPC strategy on the battery energy storage system’s state of health. By ensuring balanced currents, the battery packs connected to each phase experience uniform charging and discharging rates, preventing cell degradation due to uneven stress. This uniformity extends the overall lifespan of the battery energy storage system, reducing maintenance costs and improving economic viability. Moreover, the fast transient response of SMC-MPC allows the system to quickly compensate for sudden changes in renewable generation or load, enhancing grid stability. For instance, in a DC microgrid with solar PV and a battery energy storage system, the converter can swiftly regulate power flow during cloud cover or load switching, maintaining voltage levels within acceptable limits.
In conclusion, the proposed SMC-MPC current sharing control strategy for three-phase interleaved bidirectional Buck-Boost converters demonstrates significant advantages in battery energy storage system applications. The integration of sliding mode control in the voltage loop provides robustness against disturbances and parameter variations, while model predictive control in the current loop ensures precise and fast current tracking. Theoretical analysis, simulations, and experimental results confirm that SMC-MPC outperforms traditional PI-MPC in terms of current sharing accuracy, dynamic response, and overshoot reduction. The strategy is computationally efficient, scalable to multi-phase systems, and enhances the reliability and longevity of battery energy storage systems. Future work may explore adaptive tuning of sliding coefficients and predictive model parameters to further optimize performance under varying operating conditions. Overall, this research contributes to the advancement of control technologies for sustainable energy systems, supporting the widespread adoption of battery energy storage systems in modern power grids.