# Practical Dead-Time Control Methodology of a Three-Phase Dual Active Bridge Converter for a DC Grid System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, the large-scale integration of renewable energy sources poses an increasingly significant challenge to power system stability [1]. The reasons for the degradation in grid stability as the power production from renewable energy sources increases are several [2]:

- ▪
- System Flexibility: The large-scale integration of renewable energy sources implies potentially significant power injections during peak load times that require more system flexibility to balance energy supply and demand.
- ▪
- Integration of Inverter-Connected Devices: Another challenge for the energy transition is the mandatory integration of inverter-connected devices. Including these devices can reduce system inertia and fault current, decreasing the overall system stability.
- ▪
- Decreased Grid Inertia: The conventional power grid heavily relies on the inertia of large rotating turbines and generators of traditional power plants to provide this frequency stability. As these sources are replaced with inertia-less renewable energy sources, alternative methods to maintain frequency stability become necessary.

## 2. Analysis of the Three-Phase Dual Active Bridge Converter

#### 2.1. Basic Operation Principles of Three-Phase Dual Active Bridge Converter

_{PS}

_{M}(=ɸ/π), and this term controls the transmission power. A six-step phase voltage waveform of each bridge, the HVS, and LVS is generated under the steady-state operation [10,16]. In this paper, several assumptions are also considered for the analysis as follows:

- ▪
- The input and output voltage are constant.
- ▪
- All the coupling inductances are the same in each leg.
- ▪
- The parasitics are constant and the same in the same power switches.
- ▪
- The transformer’s magnetizing inductance is infinite.

_{C,x}is the coupling inductance of each phase, v

_{H}is the phase voltage of HVS, v

_{L}is the phase voltage of LVS, and n is the turn ratio. Under the steady state, because the initial current value of coupling inductance in i

_{Lc,x}(0) is the same value in -i

_{L}(π) according to the flux balancing law, the initial phase current of i

_{Lc,x}(0) can be expressed as follows:

_{in}is the input voltage, m is the voltage gain (=nV

_{out}/V

_{in}), and f

_{Sw}is the switching frequency. Based on (2), the initial phase current and the phase current during the switching period can be expressed mathematically and the transmit power P

_{Out}under SPS modulation can be expressed as follows:

_{PS}

_{M}range. Theoretically, the maximum transmit power of the 3P-DAB converter can be obtained when the ɸ

_{PS}

_{M}is ±1/2, such as for the SP-DAB converter. However, the ɸ

_{PS}

_{M}approaches ±1/2, where the nonlinearity of the output power is greater than that of the lower ɸ

_{PS}

_{M}because the trajectory of the output power from the ɸ

_{PS}

_{M}is parabolic. This means that if the ɸ

_{PS}

_{M}is higher than 1/3, the proportion of reactive power increases so even if the ɸ

_{PS}

_{M}changes from 0 to ±1/2 and the power is transmitted seamlessly, the ɸ

_{PS}

_{M}is usually limited to ±1/3.

#### 2.2. The Analysis of Soft-Switching Mechanism and Dead Time

_{Lc,x}(0) and i

_{Lc,x}(ɸ

_{PS}

_{M}), respectively, in Figure 3. Ideally, the inequalities of (*) enable ZVS conditions on the power switches. However, despite the higher energy of the inductance, the turn-on loss of each bridge can occur depending on individual oscillation and switching timing. The magnitude of the current in (4) is not sufficient to fully charge and discharge the parasitic output capacitance of power switches (C

_{eos}) in practice. Therefore, it is necessary to reconfigure the ZVS condition considering the minimum current for switching activity. The resonance should be analyzed and the ZVS condition can be redefined. Figure 4 shows the equivalent circuit of a 3P-DAB converter when the HVS switches of S

_{3}and S

_{6}, the LVS switches of Q

_{1}, Q

_{3}, and Q

_{6}are on-state, and S

_{1}and S

_{2}is in switching. The resonance occurs between C

_{eos}and L

_{C}

_{,1,2,3}. Here, the coefficient of C

_{eos}is two because the top and bottom of the same bridge arm are asymmetrically turn-on and turn-off mechanisms. By applying the superposition to the circuit, the resonance can be analyzed and the ZVS condition can be redefined as follows [10]:

_{eos}and, based on Equation (5), the minimum dead time can be derived.

## 3. Dead-Time Effect of Three-Phase Dual Active Bridge Converters

#### 3.1. Analysis of the Dead-Time Effect in Three-Phase Dual Active Bridge Converters

_{PS}

_{M}. Figure 6a presents the gate signal, the phase voltage, and the phase current waveform under extremely light load conditions. When the transmitted power is too small compared with the rated power, the actual ɸ

_{PS}

_{M}is too small and shorter than the dead time, causing an abnormal waveform for the phase current, as shown in Figure 6a, and increasing the reactive power, peak current, and turn-off current. Figure 6b shows the measured waveforms of the phase voltage and phase current waveforms as in the conditions in Figure 6a. In Figure 6b, it is seen that even if the output voltage is well controlled as the reference voltage 278 V, the current waveform is abnormal, which is different from Figure 3. This is because the polarity of effective ɸ

_{PS}

_{M}is negative as shown in red circle on Figure 6b, even though the calculated ɸ

_{PS}

_{M}is positive. This means that the effective phase shift angle under extremely light load conditions is shorter than the dead time as shown in Figure 6a, and it significantly affects the current waveform when the polarity of the switch current is changed during the dead time. When the dead-time effect significantly affects the 3P-DAB converter, as shown in Figure 6, since the effective phase shift is reduced, the practical output power does not match the theoretical Equation (3).

#### 3.2. Proposed Practical Dead-Time Control Methodology

_{d_critical}. Here, t

_{d_critical}is defined as a switching transition time in which an arm-short phenomenon does not occur. As the ɸ

_{PS}

_{M}increases, the dead time increases linearly from t

_{d_critical}to the critical point of the ZVS t

_{d_ZVS}. From (5), the minimum ɸ

_{PS}

_{M}for soft switching can be derived and calculated as 0.09715 based on Table 1. After passing t

_{d_ZVS}, the dead time is reduced according to (7). As the dead time decreases, the dead time matches t

_{d_critical}. Here, the dead time is limited to t

_{d_critical}in order to prevent short-circuit phenomena.

## 4. Experimental Results and Analysis of Results

_{C}

_{,1}, L

_{C}

_{,2}, and L

_{C}

_{,3}) are connected in series to the transformer. Film capacitors (K3490070106K0L155) (KENDEIL, Gallarate, Italy) that have relatively lower ESRs are used for the input and output filters. The TMS320F28335 (Texas Instruments, Dallas, TX, USA) is used as a digital controller. The parameters of the prototype 3P-DAB converter are listed in Table 1.

_{PS}

_{M}can be different. As explained in Section 3, since the conventional dead time is longer than ɸ

_{PS}

_{M}, the abnormal current waveform occurs in Figure 13a. Based on the proposed dead-time control algorithm, the experimental waveform is normal under extremely light load conditions. Since the abnormal current increases the reactive power and conduction loss, the efficiency could be improved by using the proposed algorithm. Figure 15 presents the experimental results in steady-state operation according to the output load variations. In Figure 15a, even though the effective ɸ

_{PS}

_{M}is measured very small as about 118 m° under 2 kW, the current waveform is detected as normal operation. The measured output power and the phase shift terms between the phase voltage are given in each figure. The angle of the phase shift changes according to the change in the output power. As the output load increases, the angle of the phase shift increases, as shown in (3a). Through the overall load ranges, the output power voltage is well adjusted to a reference voltage of 278 V. Figure 16 shows the comparison of the efficiency curve depending on the dead-time control. The difference between the conventional dead-time control and the proposed dead-time control is in the extremely light load conditions. The biggest difference in power conversion efficiency between the two dead-time control methods is almost 1% under extremely light load conditions. Since the dead time is the same in light load conditions, the efficiency is almost the same except for the measurement error. The highest efficiency measured is 97.22% at about 6 kW.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Theoretical switching sequence waveform according to different dead times under the steady-state operation of the 3P-DAB converter: ① a lack of minimum current with proper dead time for ZVS, ②-1 a sufficient current with a long dead time for ZVS, ②-2 an insufficient current with a long dead time for ZVS, and ③ proper current and proper dead time for ZVS.

**Figure 6.**Abnormal phase current waveforms of the 3P-DAB converter under extremely light load conditions. (

**a**) Theoretical waveform. (

**b**) Experimental results of abnormal results.

**Figure 8.**Simulation results for phase current waveforms of a 3P-DAB converter under the same light load conditions according to dead time: (

**a**) 2 μs and (

**b**) 1.25 μs.

**Figure 10.**Comparison of dead-time control between the conventional dynamic dead-time control and proposed practical dead-time control with the theoretical required dead time based on Table 1.

**Figure 12.**Photographs of experimental set-up: (

**a**) Bi-directional power supply. (

**b**) Resistance load bank.

**Figure 13.**Experimental waveforms of the 3P-DAB converter based on the different dead-time control algorithms under the same power conditions (850 W): (

**a**) conventional dead-time control and (

**b**) proposed dead-time control.

**Figure 14.**Efficiency results of the 3P-DAB converter based on the different dead-time control algorithms under the same power conditions (850 W): (

**a**) conventional dead-time control and (

**b**) proposed dead-time control.

**Figure 15.**Experimental waveforms of the 3P-DAB converter in steady-state operation using the proposed controller: (

**a**) 1 kW, (

**b**) 3 kW, (

**c**) 15 kW, and (

**d**) 25 kW.

**Figure 16.**Efficiency comparison curve between the conventional dead-time control and the proposed dead-time control algorithm.

**Figure 17.**Steady-state operation waveform according to output power under light load conditions: (

**a**) 1 kW and (

**b**) 2.5 kW.

Symbol | Quantity | Value |
---|---|---|

V_{in} | Input voltage | 550 V |

V_{out} | Output voltage | 278 V |

m | Voltage gain | 0.986 |

f_{SW} | Switching frequency | 8 kHz |

P_{o,rated} | Rated power | 25 kW |

Lc_{,x} | Coupling inductance | 43.7 μH (CH740060) |

C_{oes} | Effective output capacitance of Power switches | 4 nF |

N_{L} | Turns | 13 |

- | Transformer material | Nano-crystalline |

N_{P}:N_{S} | Turn ratio | 39:20 |

R_{S}_{,}_{HVS} | Parasitic resistor on LVS | 850 mΩ |

R_{S,LVS} | Parasitic resistor on HVS | 380 mΩ |

Cof | Output filter capacitance | 1.4 mF |

ESR | Equivalent series resistance | 138 mΩ |

t_{d} | Dead time | Variable |

- | Controller | TMS320F28335 |

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## Share and Cite

**MDPI and ACS Style**

Choi, H.-J.; Ahn, J.-H.; Jung, J.-H.; Song, S.-G.
Practical Dead-Time Control Methodology of a Three-Phase Dual Active Bridge Converter for a DC Grid System. *Energies* **2023**, *16*, 7679.
https://doi.org/10.3390/en16227679

**AMA Style**

Choi H-J, Ahn J-H, Jung J-H, Song S-G.
Practical Dead-Time Control Methodology of a Three-Phase Dual Active Bridge Converter for a DC Grid System. *Energies*. 2023; 16(22):7679.
https://doi.org/10.3390/en16227679

**Chicago/Turabian Style**

Choi, Hyun-Jun, Jung-Hoon Ahn, Jee-Hoon Jung, and Sung-Geun Song.
2023. "Practical Dead-Time Control Methodology of a Three-Phase Dual Active Bridge Converter for a DC Grid System" *Energies* 16, no. 22: 7679.
https://doi.org/10.3390/en16227679