In the context of DC microgrids, wind and photovoltaic power generation are widely deployed in distributed generation systems. Energy storage cells and supercapacitors serve as the core energy storage units in such systems. Bidirectional DC-DC converters act as the interface between the generation system and energy storage cells, playing a critical role in enhancing grid stability. Through bidirectional DC-DC converters, energy storage cells achieve bidirectional power flow with the DC bus, thereby balancing the power demands caused by distributed sources and load variations. Therefore, optimizing converter control to improve the stability and rapidity of distributed generation systems has become a research hotspot. Multi-phase interleaved parallel bidirectional DC-DC converters are widely adopted between the DC bus and energy storage cells in distributed generation and DC microgrids due to their low switch current stress, low switching loss, and high power density. However, due to parasitic parameter mismatches among parallel phases, the current stress of each phase differs, and devices experiencing higher current stress are more prone to damage, leading to malfunction of the entire parallel system. Hence, it is crucial to develop an interleaved parallel bidirectional DC-DC converter that can accommodate high current, exhibit low output ripple, high reliability, fast response, and achieve balanced phase current control.
To solve the phase-to-phase current imbalance problem in multi-phase interleaved parallel bidirectional DC-DC converters caused by parasitic parameter mismatches, and to enhance their application value in energy storage systems, various current sharing control methods have been proposed by researchers worldwide. Traditional PI-based dual-loop control suffers from slow system response, poor robustness, and complex parameter tuning. Some works have introduced a maximum current method to allow independent module operation, but dynamic performance remains limited. Others designed duty cycle allocation algorithms using neural network-based active disturbance rejection control to improve response speed and steady-state accuracy, yet the control algorithm is complex and transient current sharing was not addressed. Dynamic sleep control strategies have been proposed to extend switch lifetime, but current sharing accuracy degrades. Some approaches compensate duty cycles based on parasitic resistances in each branch to achieve current balancing, but dynamic performance is restricted. Equivalent transfer functions of voltage loop gain and open-loop output impedance are used as controlled objects for current sharing controller design, but the simplified mathematical model and limited current sensor accuracy introduce sampling errors, increasing converter complexity, cost, and failure rate. PI-Model Predictive Control (PI-MPC) applied to two-phase interleaved bidirectional converters improves closed-loop performance and dynamic response, but computational burden is high and anti-disturbance capability and current sharing accuracy still need enhancement.
This paper proposes a current sharing control strategy based on Sliding Mode Control and Model Predictive Control (SMC-MPC) for a three-phase interleaved parallel bidirectional Buck-Boost converter. Sliding mode control is applied in the voltage outer loop to replace PI control, while model predictive control is used in the current inner loop. This strategy significantly improves current sharing response speed, accuracy, steady-state performance, and transient current balancing. Simulation and experimental results demonstrate the effectiveness of the proposed method compared to PI-MPC.
For this research, we consider the energy storage cell application scenario where the bidirectional converter interfaces between a low-voltage side (e.g., battery) and a high-voltage side (e.g., DC bus). The energy storage cell voltage range is 10–40 V, and the output voltage is regulated to 50 V. The three-phase interleaved topology reduces input/output current ripple and improves power density.
Converter Topology and Characteristics
The topology of the three-phase interleaved parallel bidirectional Buck-Boost converter is illustrated in Figure 1 (not shown here). It consists of three identical single-phase Buck-Boost circuits connected in parallel. Each phase includes an energy storage inductor L1, L2, L3, power switches S1–S6 with their antiparallel diodes, and input/output filter capacitors C1 and C2. The converter can operate in Boost mode (energy flow from input to output) or Buck mode (energy flow from output to input). In Boost mode, switches S1, S3, S5 are controlled with a 120° phase shift, while S2, S4, S6 act as synchronous rectifiers (or their antiparallel diodes conduct). Similarly, in Buck mode, S2, S4, S6 are the main switches with phase-shifted control.
Table 1 summarizes the input/output current and voltage ripple expressions for the converter in different operating modes across the full duty cycle range. The ripple frequency is three times the switching frequency due to interleaving.
| Mode | Duty cycle range | Input current ripple Δiin (Boost) / Δio (Buck) | Output voltage ripple ΔUC2 (Boost) / ΔUC1 (Buck) |
|---|---|---|---|
| Boost | 0 < DBoost < 1/3 | Δiin = (Uo(1-3DBoost)DBoostTs)/L | ΔUC2 = (Uo(1-3DBoost)DBoostTs)/(3RC(1-DBoost)) |
| 1/3 ≤ DBoost ≤ 2/3 | Δiin = (Uo(3-2DBoost)(3DBoost-1)Ts)/(3L) | ΔUC2 = (Uo(3-2DBoost)(3DBoost-1)Ts)/(9RC(1-DBoost)) | |
| 2/3 < DBoost ≤ 1 | Δiin = (Uo(1-3(1-DBoost))(2DBoost-1)Ts)/L | ΔUC2 = (Uo(3-2DBoost)Ts)/(3RC) | |
| Buck | 0 < DBuck < 1/3 | Δio = (Uo(1-3DBuck)DBuckTs)/L | ΔUC1 = (Uin(1-3DBuck)2Ts2)/(24C1L) |
| 1/3 ≤ DBuck ≤ 2/3 | Δio = (Uo(3-2DBuck)(3DBuck-1)Ts)/(3L) | ΔUC1 = (Uin(3-2DBuck)(3DBuck-1)Ts2)/(36C1L DBuck) | |
| 2/3 < DBuck ≤ 1 | Δio = (Uo(1-3(1-DBuck))(2DBuck-1)Ts)/L | ΔUC1 = (Uin(1-3(1-DBuck))(2DBuck-1)Ts2)/(24C1L DBuck) |
Taking Boost mode with duty cycle in the range 2/3 < DBoost ≤ 1 as an example, the main operating waveforms are shown in Figure 2 (not shown). Gate drive signals for S1, S3, S5 are 120° phase-shifted. The input current is the sum of the three inductor currents, and its ripple frequency is three times the switching frequency.
Since the three-phase interleaved topology consists of three identical single-phase Buck-Boost converters, we derive the model for one phase. The continuous state-space equations in Boost mode are given by Eqs. (1) and (2) (not shown here). Using the linear time-invariant system discretization theorem, the discrete state-space equations are obtained as Eqs. (3)–(5) for Boost mode. Similarly, for Buck mode, Eqs. (6)–(8) are derived.
For the proposed current sharing strategy, we adopt the SMC-MPC method. The voltage outer loop uses sliding mode control to generate the reference inductor current for each phase. The current inner loop uses model predictive control to calculate the optimal duty cycle for each switch based on the reference current, thereby balancing the phase currents.
Sliding Mode-Model Predictive Control Current Sharing Strategy
Improved Maximum Current Method
The traditional maximum current sharing method, also known as automatic master-slave current sharing, typically uses PI dual-loop control. In this paper, we propose an SMC-MPC strategy where the voltage outer loop controller is a sliding mode controller, and the current inner loop is a model predictive controller. The block diagram of the control strategy is shown in Figure 4 (not shown). The sliding mode controller takes the steady-state error of each phase current, output voltage deviation, and integral of output voltage deviation as inputs, and outputs the reference inductor current for each phase. The model predictive controller takes the reference inductor current and the sampled phase current, output voltage, and input voltage to compute the optimal duty cycle for each phase. A maximum current sharing module modifies the reference current based on the actual phase current deviations. When deviations increase, the sliding mode controller increases the reference current, leading to a larger duty cycle from the MPC, thus regulating the phase currents toward balance. When deviations become zero, the reference currents are optimal, and the duty cycles achieve perfect current sharing.
Current Inner Loop Predictive Model
From the discrete state-space equations, we can predict the inductor current and output voltage at the (k+1)-th sampling instant. Under steady-state conditions, Eq. (5) can be rearranged to give the relationship between inductor current and output voltage, Eq. (9). The objective evaluation function for the current inner loop MPC is defined as:
$$Q = (U_o(k+1)-U_{o,ref})^2 + (i_{L1}(k+1)-i_{L1,ref})^2$$
Substituting Eqs. (4) and (5) into the evaluation function yields:
$$Q = \left[ \frac{1-D_{Boost1}(k)}{C_2} T_s i_{L1}(k) + \left(1-\frac{T_s}{RC_2}\right)U_o(k) – U_{o,ref} \right]^2 + \left[ i_{L1}(k) + \frac{1-D_{Boost1}(k)}{L_1}T_s U_o(k) + \frac{T_s}{L_1}U_{in}(k) – i_{L1,ref} \right]^2$$
Taking the partial derivative of Q with respect to DBoost1(k) and setting it to zero gives the optimal duty cycle expression. After simplification, the optimal duty cycle for phase 1 in Boost mode is:
$$D_{Boost1}(k) = \frac{U_o(k)i_{L1}(k)}{C_2 U_o(k)^2 T_s}(L_1 C_2 + L_1 C_2) + \frac{C_2 L_1 U_o(k) i_{L1,ref} – C_2 L_1 i_{L1}(k) U_{o,ref}}{C_2 U_o(k)^2 T_s} + \frac{C_2 T_s U_o(k)U_{in}(k)}{C_2 U_o(k)^2 T_s} – \frac{L_1 i_{L1}(k)}{C_2 U_o(k) T_s} + \cdots$$
To avoid the dependence on load resistance R, we use the relationship R = Uo/io. Substituting and simplifying yields the final expression in Eq. (15). Similarly, duty cycles for phases 2 and 3 in Boost mode (Eqs. (16), (17)) and for Buck mode (Eqs. (18)–(20)) are derived.
Outer Sliding Mode Control Model
The sliding mode surface S is designed as a linear combination of state variables: inductor current error, output voltage error, and integral of output voltage error. The state vector is:
$$\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} \sum_{m=1}^3 (i_{Lm,ref} – i_{Lm}) \\ U_{o,ref} – U_o \\ \int (U_{o,ref} – U_o) dt \end{bmatrix}$$
The sliding surface S = Δ1x1 + Δ2x2 + Δ3x3, where Δ1, Δ2, Δ3 are positive sliding coefficients chosen as p with 1/2 < p/q < 1 (q positive odd). Setting S=0 and solving for the reference inductor current yields:
$$i_{L,ref} = \frac{1}{\Delta_1} \left[ -\Delta_2 (U_{o,ref} – U_o) – \Delta_3 \int (U_{o,ref} – U_o) dt \right] + \sum_{m=1}^3 i_{Lm}$$
This reference current is then used by the MPC inner loop.
Simulation Results and Analysis
Simulations were conducted in Matlab/Simulink with parameters listed in Table 2. The switching frequency is 20 kHz, control step 0.05 s. PI parameters: Kp=0.1, Ki=20.
| Parameter | Value |
|---|---|
| Input voltage Uin | 10–40 V |
| Output voltage Uo | 50 V |
| Inductor L1 | 0.82 mH, parasitic R1=0.08 Ω |
| Inductor L2 | 0.80 mH, parasitic R2=0.10 Ω |
| Inductor L3 | 0.78 mH, parasitic R3=0.12 Ω |
| Filter capacitor C | 470 μF |
| Switching frequency fs | 20 kHz |
Current Sharing Performance Comparison
Figure 6 and 7 (not shown) present the three-phase inductor current waveforms at duty cycle 0.5 for Boost and Buck modes, comparing PI-MPC and SMC-MPC. The SMC-MPC strategy significantly reduces overshoot and improves current sharing accuracy. Table 3 quantifies the improvements.
| Control method | Mode | Overshoot (%) | Settling time (ms) | Current imbalance error (%) |
|---|---|---|---|---|
| PI-MPC | Buck | 32.8 | 13 | 3.56 |
| PI-MPC | Boost | 30.3 | 15 | 2.37 |
| SMC-MPC | Buck | 0 | 5 | 2.69 |
| SMC-MPC | Boost | 0 | 5 | 1.98 |
In Boost mode, SMC-MPC reduces overshoot by 30.3%, settling time by 66.7%, and current imbalance by 16.5%. In Buck mode, overshoot is reduced by 32.8%, settling time by 61.5%, and imbalance by 24.4%.
Load Transient Response
Load disturbances were applied at t=0.05 s and t=0.1 s. Figure 8 and 9 (not shown) depict the load jump and output voltage waveforms in Boost and Buck modes. With SMC-MPC, the output voltage quickly recovers with negligible overshoot, demonstrating strong robustness.
Experimental Results
A 500 W experimental prototype was built based on the three-phase interleaved bidirectional Buck-Boost converter topology. The main switches are Infineon IRF3205PBF MOSFETs, and the control board uses TI TMS320F28335 DSP. Hall sensors measure phase currents. Table 4 lists the prototype parameters.
| Parameter | Value |
|---|---|
| Input voltage Uin | 10–48 V |
| Output voltage Uo | 48 V |
| Switching frequency fs | 20 kHz |
| Inductors L1, L2, L3 | 0.90 mH each |
| Capacitors C1, C2 | 470 μF |
Closed-Loop Tests
Figures 11 and 12 (not shown) illustrate the three-phase inductor current waveforms for Boost mode at duty cycle 0.3 and Buck mode at duty cycle 0.7, comparing PI-MPC and SMC-MPC. Tables 5 and 6 summarize the current sharing errors.
| Control strategy | Phase | Average current (A) | Error (%) |
|---|---|---|---|
| PI-MPC | a | 2.45 | 4 |
| b | 2.09 | 4 | |
| c | 2.41 | 4 | |
| SMC-MPC | a | 2.32 | 2 |
| b | 2.35 | 2 | |
| c | 2.29 | 2 |
| Control strategy | Phase | Average current (A) | Error (%) |
|---|---|---|---|
| PI-MPC | a | 5.12 | 4 |
| b | 4.96 | 4 | |
| c | 4.98 | 4 | |
| SMC-MPC | a | 4.95 | 1 |
| b | 4.92 | 1 | |
| c | 4.86 | 1 |
The experimental results confirm that SMC-MPC achieves a maximum current sharing error of 2% in Boost mode and 1% in Buck mode, superior to PI-MPC’s 4% in both modes.
Dynamic Tests
Load jump experiments were performed. In Buck mode, load changed from 0.4 Ω to 0.8 Ω and back (Figure 13, not shown). In Boost mode, load changed from 20 Ω to 10 Ω and back (Figure 14, not shown). The three-phase currents quickly settle to balanced values. Figure 15 (not shown) compares dynamic response of SMC-MPC and PI-MPC for a load step from 2.4 Ω to 1.2 Ω and back in Buck mode. Table 7 summarizes the dynamic parameters.
| Control strategy | Overshoot (%) | Min settling time (ms) | Current imbalance error (%) |
|---|---|---|---|
| SMC-MPC | 0 | 0.4 | 2 |
| PI-MPC | 11.5 | 50 | 4 |
The proposed SMC-MPC exhibits zero overshoot, settling time of only 0.4 ms, compared to 11.5% overshoot and 50 ms settling time for PI-MPC. This demonstrates significantly improved dynamic performance and robustness.
Conclusion
This paper has presented a novel current sharing control strategy based on sliding mode control and model predictive control for a three-phase interleaved parallel bidirectional Buck-Boost converter used in energy storage cell applications. The following conclusions are drawn:
- Compared with PI-MPC, the proposed SMC-MPC strategy’s control parameters depend only on converter inherent parameters, reducing tuning complexity.
- Across the full duty cycle range and in both Boost and Buck modes, the proposed method achieves balanced inductor currents with higher accuracy. The maximum current sharing error is reduced to 2% in Boost mode and 1% in Buck mode, compared to 4% with PI-MPC.
- Under load disturbances, the proposed strategy simultaneously achieves phase current balancing and rapid output current stabilization, with zero overshoot and settling time as low as 0.4 ms, whereas PI-MPC exhibits 11.5% overshoot and 50 ms settling time. This demonstrates superior robustness and dynamic performance, which is critical for the reliable operation of energy storage systems.
The effectiveness and feasibility of the proposed SMC-MPC current sharing strategy for energy storage cell bidirectional converters have been validated through comprehensive simulations and experiments. The method offers a promising solution for high-performance power conversion in renewable energy and microgrid systems where energy storage cells play a vital role.