State-Plane Trajectory-Based Duty Control of a Resonant Bidirectional DC/DC Converter with Balanced Capacitors Stress
Abstract
:1. Introduction
- An in-depth design is presented of the novel bidirectional dual transformer-based resonant DC/DC converter featuring equivalent voltage stress distribution of the resonant capacitors. As a result, the designed approach enhances the efficiency of the DC/DC power conversion along with improved overall reliability with a lower active components count.
- A state-plane trajectory theory-based control law has been derived for proper control of the bidirectional DC/DC resonant converter. The proposed controller consists of two control terms, i.e., a feedforward term and a feedback term. Notably, a feedforward term is obtained using the state-plane trajectory theory for effectively mitigating the resonant converter nonlinearities.
- The introduction of a fixed 50% control duty cycle on the primary-side results in theoretically zero input current ripples. Consequently, the harmonics contents of the primary-side current are considerably diminished, providing significant benefits for applications involving battery charging.
- The proposed design and control strategy effectively address the variations in the leakage inductance of the two transformers. A comprehensive discussion is provided on the implications of these variations on the converter topology for different transformer connections. Furthermore, the designed control law is described, highlighting how it effectively compensates for these variations.
2. Topology Description and Detailed Operational Mode Analysis
2.1. Proposed Topology Description and Detailed Operational Mode Analysis
- The output capacitor (CS) and clamp capacitor (CDC) are significantly larger than the resonant capacitors (Cr1~Cr4).
- The transformers (T1 and T2) consist of magnetizing (Lm1, Lm2) and leakage inductances (Llk1, Llk2).
- A negligibly small dead time (Tdead) is considered.
- The resonant capacitance (Cr) consists of two identical capacitors (i.e., Cr = Cr1 + Cr2), whereas Cr1~Cr4 are identical.
2.2. Converter Analysis under Different Operation Modes
- Interval 1 [t0–t1]: During the first interval, S1 and S4 are switched on, and vab in (3) is applied across the primary windings of T1 and T2. At time t = t0, both inductors (Lr1,2) are charged with resonant currents (iLr1 = iLr2 = iLr1,2). The state equations can be modeled as
- Interval 2 [t1–t2]: At t = t1, S5 turns off while T1 and T2 continue to output −nvCdc for the rest of the half cycle (i.e., 0.5 × Tsw). At the same time, iLr1,2 start flowing through the body diode of S6. The energy stored in Lr1,2 is released during t = [t1–t2], and the trajectory moves from point y1 (at t = t1) to x2 (at t = t2). The state equations can be expressed as
- Interval 3 [t2–t3]: At t = t2, iLr1,2 become zero, and the proposed converter switches into discontinuous conduction mode (DCM) (see Figure 3). Note that iLr1,2 turn zero just before the start of Interval 3, so the body diode of S6 turns off with zero current switching (ZCS). A zero reverse recovery current flowing through each body diode helps significantly reduce the turn-off loss of the device. Note that during Interval 3, the trajectory stays at point x2, the inductor currents (iLr1,2) remain zero, and the resonant capacitors maintain the voltage (vCr1,3) at their maximum value (i.e., VS/2).
- Interval 4 [t3–t4]: At the end of the third interval, S1 and S4 (on the primary side) are turned off, where S4 achieves ZVS turn-off as iL2 was flowing at t3. In this interval, the inductor current can be written as
3. Feedforward State-Plane Trajectory-Based Control Derivation and Parameter Design Guidelines
3.1. Trajectory-Based Feedforward Term (Uff) Derivation
3.2. Overall Control Law and Its Implementation Steps
3.3. Converter Analysis under Parameters Mismatch
3.4. Key Components Design Guidelines
3.4.1. Interleaved Inductors (L1,2) Design
3.4.2. Transformer Turns Ratio (n1,2) Design
3.4.3. Resonant Components (Lr1,2 and Cr1~4) Selection
4. Experimental Verification and Discussion
4.1. Experiment Prototype Details and Validation Conditions
- Scenario I: Forward direction load transient operation (i.e., 30% (962 W) → 80% (2672 W) → 30% (962 W)) with VP (input) = 190 V for VS (output) = 380 V.
- Scenario II: Load transient under backward operation (i.e., 15% (480 W) → 65% (2200 W) → 15% (480 W)) with VS (input) = 170 V for VP (output) = 400 V.
- Scenario III: Reliability, voltage stress, and efficiency analysis.
4.2. Converter Analysis under Forward Direction Load Transient Operation (Scenario I)
4.3. Performance Analysis under the Backward Operation with Primary-Side Load Transient Change (Scenario II)
4.4. Reliability, Voltage Stress, and Efficiency Analysis (Scenario III)
4.5. Comparative Analysis of the Proposed Converter with Existing Dual Transformer-Based Isolated DC/DC Converter Topologies
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Variable [Symbol] | Value [Unit] | |
---|---|---|
Rated power [PRated] | 3.3 [kW] | |
Secondary-side voltage [VS] | 360~400 [V] | |
Primary-side voltage [VP] | 150~220 [V] | |
Switching frequency [fsw] | 50 [kHz] | |
Resonant capacitances [Cr1~4] | 200 [nF] | |
Resonant inductances [Lr] | 9.8 [uH] | |
Transformers [n1,2] (T1 [Lm1, Llk1]), (T2 [Lm2, Llk1]) | 17:24 | (1.11 [mH], 1.63 [uH]) (1.12 [mH], 1.72 [uH]) |
Input inductances [L1, L2] | 1 [mH] | |
Resonant frequency [fr1,2] | 71 [kHz] | |
DC-link capacitance [CDC] | 4.4 [uF] | |
MOSFET switches [S1~S6] | UJ3C065030K3S |
Parameter | [18] | [21] | [22] | [28] | [29] | Proposed |
---|---|---|---|---|---|---|
Components | 6S, 4C | 6S, 3C, 2D | 4S, 3C, 4D | 10S, 3C | 4S, 3C, 4D | 6S, 5C |
Efficiency | 95% | 96.3% | 98.5% | 94% | 95.3% | 97.3% |
Control Type | PI duty and phase shift control | PI and hysteresis control | Burst mode control | PI duty and phase shift control | PI phase shift control | State-plane trajectory-based control |
Control Complexity | Medium | High | High | Medium | Simple | Medium |
Circuit Complexity | Medium | Medium | High | High | Medium | Medium |
Cost | Medium | Medium | Low | High | Medium | Medium |
Rated Power | 1 kW | 1 kW | 3.2 kW | 300 W | 1 kW | 3.3 kW |
Capacitor Voltage Balancing | Unbalanced | Unbalanced | Balanced | − | Unbalanced | Balanced |
Power Flow | Bidirectional | Unidirectional | Unidirectional | Bidirectional | Unidirectional | Bidirectional |
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Rehman, A.U.; Kim, M.; Jung, J.-W. State-Plane Trajectory-Based Duty Control of a Resonant Bidirectional DC/DC Converter with Balanced Capacitors Stress. Mathematics 2023, 11, 3222. https://doi.org/10.3390/math11143222
Rehman AU, Kim M, Jung J-W. State-Plane Trajectory-Based Duty Control of a Resonant Bidirectional DC/DC Converter with Balanced Capacitors Stress. Mathematics. 2023; 11(14):3222. https://doi.org/10.3390/math11143222
Chicago/Turabian StyleRehman, Abd Ur, Minsung Kim, and Jin-Woo Jung. 2023. "State-Plane Trajectory-Based Duty Control of a Resonant Bidirectional DC/DC Converter with Balanced Capacitors Stress" Mathematics 11, no. 14: 3222. https://doi.org/10.3390/math11143222
APA StyleRehman, A. U., Kim, M., & Jung, J. -W. (2023). State-Plane Trajectory-Based Duty Control of a Resonant Bidirectional DC/DC Converter with Balanced Capacitors Stress. Mathematics, 11(14), 3222. https://doi.org/10.3390/math11143222