# Improving the Efficiency of an Isolated Bidirectional Dual Active Bridge DC–DC Converter Using Variable Frequency

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}for the given values of the SPBR output voltage V

_{1}and nominal battery voltage V

_{2}. In a conventional battery charging process, the current I

_{2}flows from the network to the battery. When the battery energy is used to supply power to the grid, the direction of I

_{2}is the opposite [3]. It is also possible to integrate renewable energy systems and bidirectional EV chargers to facilitate smart electrification and reduce net operating costs by providing grid support and using the EV battery as a power reserve [4].

## 2. IBDC Configuration

_{1}and V

_{2}. The inductor L, which also includes the leakage inductance of the transformer, serves as the instantaneous energy storage device. The duty ratio of the switching signal is 50%, but there is a phase shift ϕ between primary and secondary bridges that defines the amplitude and direction of the power flow. C1 is the DC link capacitor connected to the output voltage V

_{1}of the SPBR and C2 is the output capacitor of the DAB-IBDC. In this point of voltage V

_{2}, the EV battery is connected. In charge mode, the power flows from C1 to C2. When the battery supplies power to the grid (discharge mode), the power flows in the opposite direction. All transistors are SiC MOSFET.

## 3. Analysis of the SPS-IBDC

_{2}

^{*}, given by

_{L}(θ) of the inductance and the output current of the primary bridge i

_{1}(θ) for any operating cycle can be determined by means of next piecewise equations:

_{2}of the battery. The power transferred during the charging or discharging process at maximum output current (positive or negative) should remain between the two curves.

## 4. Analysis of the VF-IBDC

_{min}phase where the waveforms become those shown in Figure 5.

_{2}is maintained at its maximum value for any value of battery voltage between V

_{2min}and V

_{2max}, the following design equation can be obtained to determine the value of the ratio transformer n:

_{1}/f

_{2}. Since (14) shows that power is inversely proportional to frequency, values for f

_{1}and f

_{2}are chosen in the lower part of the determined range. Given f

_{1}= 100 kHz and f

_{2}= 200 kHz, n = 1.65 is obtained.

_{2}of the battery. The power transferred at maximum output current in ZVS and ZCS condition should remain between the two curves.

## 5. Comparative Analysis of Power Losses and Efficiency

_{sw}focuses solely on the turn-off losses of the inverter bridge transistors as the turn-on switching losses are negligible due to the ZVS condition [27].

_{DS}= 1200 V and R

_{Dson}= 16 mΩ.

_{CD}

_{1}represents the conduction power losses of the primary bridge and P

_{CD}

_{2}represents the conduction power losses of secondary bridge.

_{off}provided by the manufacturer using the following polynomial function.

^{−1/2}

^{−1}

_{DI}is the core loss density of the inductor given by the manufacturer for the operating frequency and magnetic flux density, and V

_{II}is its volume. The inductor core is composed of two pieces of KOOL MU 6527 U core from Magnetics.

_{DT}is the core loss density of the transformer, and V

_{TI}is its volume. The transformer core is made with two pieces of the uncoated ferrite core U 126/91/20 from Magnetics. In both cases, the designs have been made with a flux density that guarantees non-saturation of the magnetic material. Specifically, the maximum flux density in the inductor core is 190 mT, and it is 100 mT in the transformer core.

_{IC}of the inductor, it is necessary to know the effective resistance of the winding R

_{I}taking into account the conductivity, the total length and the skin effect using

_{TC}is given by

_{T}

_{1}and R

_{T}

_{2}are the effective resistance of the primary and secondary transformer windings, respectively.

## 6. VF-IBDC Control Schema

## 7. Experimental Results

- A.
- A primary bridge with four C3M0016120K SiC MOSFETs mounted on a water cooling heatsink.
- B.
- A secondary bridge with eight C3M0016120K SiC MOSFETs mounted on a water cooling heatsink.
- C.
- An inductor L of 10.5 µH (including transformer leakage inductance).
- D.
- A transformer T with n = 10:6.
- E.
- An integrated digital electronic control on an FPGA-based system.

_{2}= 400 V) to 98 kHz (V

_{2}= 285 V). The control circuit regulates the output current of 25 A constant in both cases.

_{2}= 400 V in Figure 12a or V

_{2}= 285 V in Figure 12b with V

_{1}= 385 V. Now, the regulated current I

_{2}is −25 A. The change of frequency in discharge mode is quite similar to that in charge mode.

_{1}= 385 V when V

_{2}is 400 V (red lines) and 285 V (blue lines). The results obtained in discharge mode were very similar. Note that there are some differences between the experimental and calculated results that may be due to the modeling method used, the existence of losses of other elements not taken into account in the calculation (capacitors, conductors, parasitic components, voltage and current sensors, etc.) and also the measurement process.

## 8. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Transferred power of the SPS-IBDC versus phase shift. The red line corresponds to V

_{2}= 400 V, and the blue line corresponds to V

_{2}= 285 V.

**Figure 6.**Transferred power of the VF-IBDF converter versus switching frequency. The red line corresponds to V

_{2}= 400 V, and the blue line corresponds to V

_{2}= 285 V.

**Figure 7.**VF-IBDC’s total power losses (dashed line) and efficiency (solid line) in front of output power for V

_{2}= 400 V (red) and V

_{2}= 285 V (blue).

**Figure 8.**SPS-IBDC total power losses (dashed line) and efficiency (solid line) in front of output power for V

_{2}= 400 V (red) and V

_{2}= 285 V (blue).

**Figure 11.**Experimental waveforms of the VF-IBDC in charge mode with V

_{1}= 385 V and V

_{2}= 400 V (

**a**) when P = 10 kW and (

**b**) when P = 7125 W. C1 (dark blue) is the inductor voltage (500 V/div), C2 (magenta) is the primary bridge output current (20 A/div), and C3 (light blue) is the secondary bridge input current (20 A/div). Time base is 0.5 µs/div.

**Figure 12.**Experimental waveforms of the VF-IBDC in discharge mode with V

_{1}= 385 V and V

_{2}= 400 V (

**a**) when P = 10 kW and (

**b**) when P = 7125 W. C1 (dark blue) is the inductor voltage (500 V/div), C2 (magenta) is the primary bridge output current (20 A/div) and C3 (light blue) is the secondary bridge input current (20 A/div). Time base is 0.5 µs/div.

**Figure 13.**Calculated and experimental efficiency of VF-IBDC converter in function of normalized output power. Solid lines and marking symbols represent the experimental measurements. Dashed lines represent theoretical predictions. Dotted lines represent the evolution of the current I

_{2}during the tests.

Specification | Symbol | Value | Unit |
---|---|---|---|

Maximum Power | P_{max} | 10 | kW |

Initial Switching Frequency | f | 100 | kHz |

Regulated DC Input Voltage | V_{1} | 385 | V |

Minimum DC Output Voltage | V_{2 min} | 285 | V |

Maximum DC Output Voltage | V_{2 max} | 400 | V |

Maximum Output Current | I_{2} | 25 | A |

Magnitude | Symbol | V_{2} = 400 V | V_{2} = 285 V | Unit |
---|---|---|---|---|

Primary bridge transistor conduction losses | P_{CD}_{1} | 7.2 | 3.6 | W |

Second. Bridge transistor conduction losses | P_{CD}_{2} | 4.9 | 2.5 | W |

Primary bridge transistor switching losses | P_{SW}_{1} | 2.0 | 1.0 | W |

Second. Bridge transistor switching losses | P_{SW}_{2} | 28.7 | 8.7 | W |

Total primary bridge losses | 4(P_{CD}_{1} + P_{SW}_{1}) | 36.8 | 18.6 | W |

Total secondary bridge losses | 8(P_{CD}_{2} + P_{SW}_{2}) | 269.1 | 89.6 | W |

Total inductor core losses | P_{II} + P_{IC} | 18.6 | 2.6 | W |

Total transformer losses | P_{TI} + P_{TC} | 74.6 | 10.4 | W |

Efficiency | η | 96.2 | 98.3 | % |

Magnitude | Symbol | V_{2} = 400 V | V_{2} = 285 V | Unit |
---|---|---|---|---|

Primary bridge transistor conduction losses | P_{CD}_{1} | 9.7 | 6.2 | W |

Second. bridge transistor conduction losses | P_{CD}_{2} | 6.6 | 4.2 | W |

Primary bridge transistor switching losses | P_{SW}_{1} | 17.4 | 17.4 | W |

Secondary bridge transistor switching losses | P_{SW}_{2} | 29.0 | 17.6 | W |

Total primary bridge losses | 4(P_{CD}_{1} + P_{SW}_{1}) | 108.5 | 94.2 | W |

Total secondary bridge losses | 8(P_{CD}_{2} + P_{SW}_{2}) | 284.9 | 174.2 | W |

Total inductor losses | P_{II} + P_{IC} | 18.9 | 9.6 | W |

Total transformer losses | P_{TI} + P_{TC} | 75.8 | 38.5 | W |

Efficiency | η | 95.4 | 95.8 | % |

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**MDPI and ACS Style**

Esteve, V.; Bellido, J.L.; Jordán, J.; Dede, E.J.
Improving the Efficiency of an Isolated Bidirectional Dual Active Bridge DC–DC Converter Using Variable Frequency. *Electronics* **2024**, *13*, 294.
https://doi.org/10.3390/electronics13020294

**AMA Style**

Esteve V, Bellido JL, Jordán J, Dede EJ.
Improving the Efficiency of an Isolated Bidirectional Dual Active Bridge DC–DC Converter Using Variable Frequency. *Electronics*. 2024; 13(2):294.
https://doi.org/10.3390/electronics13020294

**Chicago/Turabian Style**

Esteve, Vicente, Juan L. Bellido, José Jordán, and Enrique J. Dede.
2024. "Improving the Efficiency of an Isolated Bidirectional Dual Active Bridge DC–DC Converter Using Variable Frequency" *Electronics* 13, no. 2: 294.
https://doi.org/10.3390/electronics13020294