# An Improved Charge-Based Method Extended to Estimating Appropriate Dead Time for Zero-Voltage-Switching Analysis in Dual-Active-Bridge Converter

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## Abstract

**:**

## 1. Introduction

## 2. Unified Equivalent Circuit for Switching Instant in DAB Converters

#### 2.1. Model of Dual-Active-Bridge Converter

#### 2.2. Unified Equivalent Circuit

## 3. Improved Charge-Based Method and Dead-Time Estimation

#### 3.1. Concept of Minimal Switching Current

#### 3.2. Derivation of Minimal Switching Current

#### 3.3. Lowest Switching Current Control

#### 3.4. Range of Dead-Time Duration for ZVS

## 4. Experimental Verification of ZVS Realization

#### 4.1. Experimental Setup

#### 4.2. Estimation of Minimal Switching Current and Dead-Time Range for ZVS

#### 4.3. Verification of ZVS Realization with Lowest Switching Current Control

#### 4.3.1. Operations without Lowest Switching Current Control

#### 4.3.2. Verification of Dead-Time Range for ZVS

#### 4.3.3. Operations with Lowest Switching Current Control and Designed Dead Time

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic waveforms of the DAB converter with the (

**a**) SPS modulation, (

**b**) EPS modulation, and (

**c**) TPS modulation.

**Figure 3.**Unified equivalent circuit of the DAB converter, in which all the possible switching instances can be analyzed.

**Figure 4.**Equivalent circuits for analyzing ZVS: (

**a**) for ${S}_{\mathrm{U}}$ turning on and (

**b**) for ${S}_{\mathrm{L}}$ turning on. The required initial directions of currents to achieve ZVS are also shown in the circuits.

**Figure 5.**Schematic waveforms of the drain–source voltages and the inductor current with a long enough dead-time period of critical switchings, (

**a**) for the condition of ${E}_{\mathrm{dc}}>0$, and (

**b**) for the condition of ${E}_{\mathrm{dc}}<0$.

**Figure 6.**Schematic view of the range of dead-time durations, ${t}_{\mathrm{d}}$, as function of ${{I}_{\mathrm{m}}}^{*}$ in the conditions of (

**a**) ${E}_{\mathrm{dc}}>0$ and (

**b**) ${E}_{\mathrm{dc}}<0$.

**Figure 7.**Overview of (

**a**) fabricated 4 kW experimental setup and (

**b**) back side of the single DAB board.

**Figure 8.**Lower and upper limits of the dead-time duration for ZVS shown as solid lines, and experimentally measured boundary operating points shown as star marks in the conditions of (

**a**) $k=0.67$ (${E}_{\mathrm{dc}}>0$), and (

**b**) $k=1.5$ (${E}_{\mathrm{dc}}<0$). Some example operating points discussed in this section are marked as A, B, C, and D, and resulting settings for operations are marked as E and F.

**Figure 9.**Zoomed waveforms around critical switching transients with the operating points outside of dead-time range for ZVS as example points, (

**a**) marked as A, (

**b**) marked as B, and (

**c**) marked as C in Figure 8.

**Figure 10.**Zoomed waveforms around critical switching transient with the operating point at the experimental minimal switching current indicated as point D in Figure 8a.

**Figure 11.**Zoomed waveforms around critical switching transients with enough margin of initial switching current and dead-time as example points (

**a**) marked as E, (

**b**) marked as F in Figure 8.

**Table 1.**List of all possible combinations of switching cases and the corresponding results of ${V}_{\mathrm{eq}}$ in phase-shift modulations.

# | Switching | Switching | Device in | ${{\mathit{V}}_{\mathbf{port}}}^{\prime}$ | ${\mathit{V}}_{\mathbf{eq}}$ |
---|---|---|---|---|---|

Leg | Motion | Adjacent Leg | |||

1 | left | upper on | + | $-{{V}_{\mathrm{port}}}^{\prime}$ | |

2 | − | $+{{V}_{\mathrm{port}}}^{\prime}$ | |||

3 | ${S}_{\mathrm{U}}$ turns on, | 0 | 0 | ||

4 | ${S}_{\mathrm{L}}$ turns off | lower on | + | refer to #8 | |

5 | − | refer to #7 | |||

6 | 0 | refer to #9 | |||

7 | upper on | + | $-{{V}_{\mathrm{port}}}^{\prime}$ | ||

8 | − | $+{{V}_{\mathrm{port}}}^{\prime}$ | |||

9 | ${S}_{\mathrm{U}}$ turns off, | 0 | 0 | ||

10 | ${S}_{\mathrm{L}}$ turns on | lower on | + | refer to #2 | |

11 | − | refer to #1 | |||

12 | 0 | refer to #3 | |||

13 | right | upper on | + | $+{{V}_{\mathrm{port}}}^{\prime}$ | |

14 | − | $-{{V}_{\mathrm{port}}}^{\prime}$ | |||

15 | ${S}_{\mathrm{U}}$ turns on, | 0 | 0 | ||

16 | ${S}_{\mathrm{L}}$ turns off | lower on | + | refer to #20 | |

17 | − | refer to #19 | |||

18 | 0 | refer to #21 | |||

19 | upper on | + | $+{{V}_{\mathrm{port}}}^{\prime}$ | ||

20 | − | $-{{V}_{\mathrm{port}}}^{\prime}$ | |||

21 | ${S}_{\mathrm{U}}$ turns off, | 0 | 0 | ||

22 | ${S}_{\mathrm{L}}$ turns on | lower on | + | refer to #14 | |

23 | − | refer to #13 | |||

24 | 0 | refer to #15 |

Rated power | P | 4 kW |

Switching frequency | ${f}_{\mathrm{sw}}$ | 20 kHz |

Input voltage | ${V}_{1}$ | 270 V ($k=0.67$) |

400 V ($k=1.5$) | ||

Output voltage | ${V}_{2}$ | 400 V ($k=0.67$) |

270 V ($k=1.5$) | ||

Leakage inductance | L | 61 $\mathsf{\mu}$H |

Transformer winding ratio | $1:n$ | $1:1$ |

Type of devices | C3M0025065D |

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**MDPI and ACS Style**

Zhang, H.; Isobe, T.
An Improved Charge-Based Method Extended to Estimating Appropriate Dead Time for Zero-Voltage-Switching Analysis in Dual-Active-Bridge Converter. *Energies* **2022**, *15*, 671.
https://doi.org/10.3390/en15020671

**AMA Style**

Zhang H, Isobe T.
An Improved Charge-Based Method Extended to Estimating Appropriate Dead Time for Zero-Voltage-Switching Analysis in Dual-Active-Bridge Converter. *Energies*. 2022; 15(2):671.
https://doi.org/10.3390/en15020671

**Chicago/Turabian Style**

Zhang, Haoyu, and Takanori Isobe.
2022. "An Improved Charge-Based Method Extended to Estimating Appropriate Dead Time for Zero-Voltage-Switching Analysis in Dual-Active-Bridge Converter" *Energies* 15, no. 2: 671.
https://doi.org/10.3390/en15020671