# Hybrid Modulation of Bidirectional Three-Phase Dual-Active-Bridge DC Converters for Electric Vehicles

^{*}

## Abstract

**:**

_{4}battery is established to validate the feasibility and effectiveness.

## 1. Introduction

_{4}battery was established to verify the proposed method.

## 2. Review of DAB Operation

#### 2.1. 3ΦDAB Phase-Shift Modulation

_{an}is a-phase voltage in the primary side and V

_{rm}’ is the secondary-side r-phase voltage V

_{rm}referred into primary-side. As can be seen, both phase voltages show a six-step square wave. The variable i

_{a}is the a-phase current that is determined according to voltage difference applied on the L

_{eqa}, which is defined as the a-phase equivalent inductance referred to the primary side. In this case, L

_{eqa}is equal to (L

_{a}+ N

^{2}L

_{r}). Thus the power transfer P

_{D}can be determined based on integrating both voltage and current. As shown in Equations (1) and (2), P

_{D}is dependent on the phase-shift angle δ between two sides of the transformer [18,21]:

_{bat}/V

_{i}), and ω is the switching frequency in radians per second. The theoretical phase-shifted angle δ for a corresponding P

_{D}also can be expressed as the following Equations (3) and (4):

#### 2.2. 3ΦDAB Trapezoidal Modulation

_{eqb}and L

_{eqc}are in parallel connection. Therefore, the total equivalent inductance L

_{eqT}can be expressed as Equation (5):

_{eqb,c}is equal to 0.5L

_{eqa}assuming equal three-phase total equivalent inductances, L

_{eqa}, L

_{eqb}and L

_{eqc}. Figure 2b shows the typical voltage and current waveforms of trapezoidal modulation. The power conversion P

_{T}can be expressed as Equations (6) and (7) [18,21]. Controllable variables include phase-shifted angle δ

_{T}, the primary- and secondary-side duty cycles D

_{1}, D

_{2}.

_{T}could be simple controlled by two variables δ

_{T}and D

_{1}. Once the variable δ

_{T}is decided, the duty cycle D

_{1}can be obtained as shown in Equation (10):

## 3. Hybrid Modulation Design

#### 3.1. Loss and Efficiency

_{mode}. Despite the power loss equations and simulation results, we still use the trial-and-error method to locate the crossover point of the efficiency curves and select 2 A as the mode-switching current I

_{mode}in the experiment. The efficiency curves and the preferred mode-switching current I

_{mode}is measured and verified in the experimental results in a later section.

#### 3.2. Control Scheme

**is set at off-state so that the modulator input is simply determined by current command I**

_{CV}_{comd}only. On the other hand, battery voltage V

_{bat}is required for CV operation. As shown, logic switch S

_{CV}is changed to on-state to produce the modified current I

_{CV}that is added to I

_{comd}for the hybrid modulator.

_{mode}, a suitable modulation, phase-shifted or trapezoidal mode, is selected to generate a phase-shifted angle and/or duty ratio. As shown, in phase-shifted modulation, the logic switch S

**is turned on to allow a PI controller generating phase angle command δ according to the current command I**

_{PS}_{comd}. On the other hand, duty ratio command D

_{1}can be produced by turning on S

**for the trapezoidal mode. The required phase angle δ**

_{TA}_{T}is the phase-shifted angle at current turning-point I

_{mode}. Figure 6b shows the mode transition of the hybrid modulator, where I

_{mode}is set as 2 A. As shown, δ and D

_{1}are controllable variables for the current command larger and less than 2 A, respectively.

_{1}and phase angle δ

_{T}in trapezoidal modulation. When switching from phase-shift to trapezoidal modulation, the phase angle δ generated by phase-shift modulation is sent to trapezoidal modulation as a fixed variable. During the trapezoidal modulation, the phase angle won’t be changed by the PI because the

**S**in Figure 6a is off. This hybrid modulator design reduces the bouncing problem between modulations.

_{PS}_{mode}. At the end of charging, CV is started instead to decrease charging current. The charging process is ended as the charging current is less than 0.4 A. For discharging requirement, only current command is needed. A low-voltage limitation 42 V is considered in this case for preventing battery from over-discharging.

## 4. Experimental Results

_{4}battery (TY-D 20-48, 20AH, Ty Dynamic Co., Ltd., New Taipei City, Taiwan) is applied to the secondary side. A three-phase transformer is composed by three single-phase ferrite-core transformers (ferrite core, EE55-28-21-MB3, New Favor Industry Co., Ltd., Taipei, Taiwan). The leakage inductance of the transformer is referred to the high-voltage side. The control strategy of the converter is accomplished via usage of a digital signal processors (DSPs, TMS320C28335, Texas Instruments, Dallas, TX, USA).

#### 4.1. Steady State

_{an}, V

_{rm}, i

_{a}waveforms when the converter is operated at I

_{B}

^{*}= 1 A. Obviously, trapezoidal modulation is enabled with parameters D

_{1}= 23.5% (11.75 μs), D

_{2}= 25.86% (11.75 μs) and δ

_{T}= 5.2° (0.72 μs). Note that the transformer current i

_{a}is approximately equal to 0.1 A due to dead time. Figure 8b shows key waveforms in phase-shifted modulation at I

_{B}

^{*}= 10 A, in which the phase angle δ is 30°. Figure 8c shows the waveforms also in phase-shifted modulation but with I

_{B}

^{*}= −10 A discharging current.

#### 4.2. Transient Behaviour

_{bat}

^{*}increases from 1 to 4 A. As expected, the modulation is successfully switched from trapezoidal mode to phase-shifted mode. Figure 9b shows the transient behavior when the charging current command I

_{bat}

^{*}is increased from 0 to 4, 6 and 8 A, respectively. As shown, the charging current I

_{bat}can is able to follow the current command I

_{bat}

^{*}.

_{comd}is tuned slowly in constant-voltage mode, so the PI controller in the hybrid modulator can be designed for fast-tracking ability with hard-to-notice overshoot transient. Since the transient experiments are extreme case of current-command-I

_{comd}adjustment, the current spikes in Figure 9b actually is the overshoot expressed in terms of 2 s/div, which is induced by the fast-tracking PI controller.

#### 4.3. CV Operation

_{bat}and battery current when the operation of the converter changes from CC mode to CV mode. The converter runs in CC mode at I

_{bat}

**= 10 A during t**

^{*}_{0}–t

_{1}period, which is modulated by the phase-shifted scheme. When the battery voltage is equal to 58.4 V at t

_{1}, the charging mode switches to CV mode. During the CV mode, the converter still operates in phase-shifted modulation during t

_{1}–t

_{2}period since the charging current I

_{bat}is larger than I

_{mode}= 2 A. When I

_{bat}is less than 2 A, the converter changes its modulation to the trapezoidal mode during the t

_{2}–t

_{3}period. After I

_{bat}is smaller than 0.4 A at t

_{3}, the battery charging is terminated.

#### 4.4. Efficiency

_{mode}= 1 A. Figure 11b gives detailed measurements of the power loss in phase-shifted mode and the result in the trapezoidal mode for light load condition. Label on1 and on2 stand for the turn-on loss of primary- and secondary-side switches, respectively; label off1 and off2 stand for the turn-off loss of primary- and secondary-side switches, respectively; the label cond1 and cond2 stand for the conduction loss of primary- and secondary-side switches, respectively; label Tr stands for the transformer loss. Transformer loss occupies over 60% loss, which might be improved by using low core loss material. This results verifies the availability of hybrid method.

## 5. Conclusions

_{4}battery is established to validate the feasibility and the effectiveness of the proposed modulation method. The results show that efficiency can be increased under light load conditions.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Theoretical waveforms of 3ΦDAB converter. (

**a**) Phase-shifted modulation; (

**b**) Trapezoidal modulation.

**Figure 4.**Modulation parameters with respect to current. (

**a**) Phase-shifted modulation; (

**b**) Trapezoidal modulation.

**Figure 5.**Simulation result of the power loss and efficiency. (

**a**) Detailed loss with phase-shift; (

**b**) Detailed loss with trapezoidal; (

**c**) The curves of power loss; (

**d**) Efficiency curve.

**Figure 6.**The control scheme and hybrid modulation. (

**a**) The control scheme of the converter; (

**b**) Phase angle and duty cycle of hybrid modulation.

**Figure 8.**Steady-state waveforms. (

**a**) Trapezoidal modulation with 1 A charging current; (

**b**) Phase-shifted modulation with 10 A charging current; (

**c**) Phase-shifted modulation with 10 A discharging current.

**Figure 9.**Transient waveforms. (

**a**) Waveforms when the modulation switches; (

**b**) Waveforms when charging current changes.

**Figure 11.**Analysis of efficiency and loss. (

**a**) Measured efficiency of the converter with hybrid modulation; (

**b**) Histogram of the power loss.

Parameter | Name | Value | Unit |
---|---|---|---|

P_{rated} | Rated power | 1.2 | kW |

f_{s} | Switching frequency | 20 | kHz |

V_{i} | Input voltage | 350 | Volt |

V_{bat} | Output voltage | 42–58.4 | Volt |

C_{snubber} | Snubber capacitors | 1.0 | nF |

L_{a} L_{b} L_{c} | HVS auxiliary inductors | 215 | μH |

L_{r} L_{s} L_{t} | LVS auxiliary inductors | 6 | μH |

L_{leakage} | Leakage inductance | 65 | μH |

N | Turn ratio | 6 | - |

R_{p} | Primary-side winding resistance of the transformor | 265 | mΩ |

R_{S} | Secondary-side winding resistance of the transformor | 102 | mΩ |

R_{ds} | Conductor Resistance of secondary-side switches | 22 | mΩ |

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**MDPI and ACS Style**

Wang, Y.-C.; Ni, F.-M.; Lee, T.-L. Hybrid Modulation of Bidirectional Three-Phase Dual-Active-Bridge DC Converters for Electric Vehicles. *Energies* **2016**, *9*, 492.
https://doi.org/10.3390/en9070492

**AMA Style**

Wang Y-C, Ni F-M, Lee T-L. Hybrid Modulation of Bidirectional Three-Phase Dual-Active-Bridge DC Converters for Electric Vehicles. *Energies*. 2016; 9(7):492.
https://doi.org/10.3390/en9070492

**Chicago/Turabian Style**

Wang, Yen-Ching, Fu-Ming Ni, and Tzung-Lin Lee. 2016. "Hybrid Modulation of Bidirectional Three-Phase Dual-Active-Bridge DC Converters for Electric Vehicles" *Energies* 9, no. 7: 492.
https://doi.org/10.3390/en9070492