# Simulations to Eliminate Backflow Power in an Isolated Three-Port Bidirectional DC–DC Converter

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Circuit Description

#### 2.2. Backflow Power in SPS Operation

#### 2.3. Backflow Power in DPS Operation

## 3. Results and Discursion

#### 3.1. Backflow Power Eliminated with DPS

#### 3.2. Characteristics of the Backflow Power and the Power Processed by the Converter

#### 3.2.1. Characterization of the Backflow Power

#### 3.2.2. Characterization of the Processed Power at the Various Ports

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DPS | Dual phase shift |

SPS | Single phase shift |

PSIM | Power SIM |

TAB | Triple active bridge |

RMS | Root mean square |

DAB | Dual active bridge |

SST | Solid state transformer |

Symbols | |

$\mathrm{D}$ | Internal phase-shift ratio |

${\mathrm{D}}_{1}$ | Phase-shift ratio between ports 1 and 2 |

${\mathrm{D}}_{2}$ | Phase-shift ratio between ports 1 and 3 |

$\mathsf{\delta}$ | Internal phase-shift angle |

${\mathsf{\delta}}_{1}$ | Phase-shift angle between ports 1 and 2 |

${\mathsf{\delta}}_{2}$ | Phase-shift angle between ports 1 and 3 |

${\mathrm{V}}_{1},{\mathrm{V}}_{2},{\mathrm{V}}_{3}$ | DC-linked voltages at the different ports |

${\mathrm{U}}_{1},{\mathrm{U}}_{2},{\mathrm{U}}_{3}$ | Voltages at the transformer terminals |

${\mathrm{N}}_{1},{\mathrm{N}}_{2},{\mathrm{N}}_{3}$ | Number of turns of the different windings |

${\mathrm{I}}_{1},{\mathrm{I}}_{2},{\mathrm{I}}_{3}$ | Transformer currents |

${\mathrm{L}}_{1},{\mathrm{L}}_{2},{\mathrm{L}}_{3}$ | Leakage inductance of the windings |

${\mathrm{I}}_{\mathrm{in}}$ | Converter’s input current |

${\mathrm{k}}_{1},{\mathrm{k}}_{2}$ | Voltage conversion ratios |

${\mathrm{P}}_{\mathrm{Rs}}$ | Backflow power with SPS control |

${\mathrm{P}}_{\mathrm{Rd}}$ | Backflow power with DPS control |

A | Area of the backflow region |

T | Switching period |

${\mathrm{I}}_{\mathrm{A}}$ | Average current |

${\mathrm{P}}_{\mathrm{R}12}$ | Backflow power between ports 1 and 2 |

${\mathrm{P}}_{\mathrm{R}13}$ | Backflow power between ports 1 and 3 |

${\mathrm{P}}_{\mathrm{s}1},{\mathrm{P}}_{\mathrm{s}2},{\mathrm{P}}_{\mathrm{s}3}$ | Power processed at the ports with SPS |

${\mathrm{P}}_{\mathrm{d}1},{\mathrm{P}}_{\mathrm{d}2},{\mathrm{P}}_{\mathrm{d}3}$ | Power processed at the ports with DPS |

${\mathrm{P}}_{\mathrm{N}}$ | Maximum possible power |

${\mathrm{p}}_{\mathrm{rs}}$ | Ratio of backflow power with SPS on ${\mathrm{P}}_{\mathrm{N}}$ |

${\mathrm{p}}_{\mathrm{rd}}$ | Ratio of backflow power with DPS on ${\mathrm{P}}_{\mathrm{N}}$ |

${\mathrm{p}}_{\mathrm{s}1},{\mathrm{p}}_{\mathrm{s}2},{\mathrm{p}}_{\mathrm{s}3}$ | Ratio of power at the ports with SPS on ${\mathrm{P}}_{\mathrm{N}}$ |

${\mathrm{p}}_{\mathrm{d}1},{\mathrm{p}}_{\mathrm{d}2},{\mathrm{p}}_{\mathrm{d}3}$ | Ratio of power at the ports with DPS on ${\mathrm{P}}_{\mathrm{N}}$ |

## References

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**Figure 8.**Characteristic of the power at the different ports for the SPS and the DPS (

**a**) at port one for SPS, (

**b**) at port one for DPS, (

**c**) at ports 2 and 3 for SPS, and (

**d**) at ports 2 and 3 for DPS.

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

DC linked voltages (v) | $\mathrm{V}$ | $400$ |

Switching frequency (kHz) | $\mathrm{f}$ | $30$ |

Turn ratio | $\mathrm{n}$ | $1:1:1$ |

Leakage inductance (µH) | $\mathrm{L}$ | $30$ |

Power (kw) | ${\mathrm{P}}_{1}$ | 10 |

Phase shift ratio | ${\mathrm{D}}_{\mathrm{m}}$ | 0.215 |

Phase shift angle | ${\mathsf{\delta}}_{\mathrm{m}}$ | 38.7° |

Internal phase shift angle | $\mathsf{\delta}$ | 20° |

Time | Value |
---|---|

${\mathrm{t}}_{0}$ | 0 |

${\mathrm{t}}_{1}$ | ${\mathrm{TD}}_{\mathrm{m}}/2$ |

${\mathrm{t}}_{2}$ | T/2 |

${\mathrm{t}}_{3}$ | T[1 + ${\mathrm{D}}_{\mathrm{m}}$]/2 |

${\mathrm{t}}_{4}$ | T |

Time | Value |
---|---|

${\mathrm{t}}_{0}$ | 0 |

${\mathrm{t}}_{1}$ | $\mathrm{TD}/2$ |

${\mathrm{t}}_{2}$ | $\mathrm{T}[\mathrm{D}+{\mathrm{D}}_{\mathrm{m}}]/2$ |

${\mathrm{t}}_{3}$ | T/2 |

${\mathrm{t}}_{4}$ | $\mathrm{T}\left[1+\mathrm{D}\right]$/2 |

${\mathrm{t}}_{5}$ | $\mathrm{T}[1+\mathrm{D}+{\mathrm{D}}_{\mathrm{m}}]/2$ |

${\mathrm{t}}_{6}$ | T |

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**MDPI and ACS Style**

Koneh, N.N.; Ko, J.-S.; Kim, D.-K.
Simulations to Eliminate Backflow Power in an Isolated Three-Port Bidirectional DC–DC Converter. *Energies* **2023**, *16*, 450.
https://doi.org/10.3390/en16010450

**AMA Style**

Koneh NN, Ko J-S, Kim D-K.
Simulations to Eliminate Backflow Power in an Isolated Three-Port Bidirectional DC–DC Converter. *Energies*. 2023; 16(1):450.
https://doi.org/10.3390/en16010450

**Chicago/Turabian Style**

Koneh, Norbert Njuanyi, Jae-Sub Ko, and Dae-Kyong Kim.
2023. "Simulations to Eliminate Backflow Power in an Isolated Three-Port Bidirectional DC–DC Converter" *Energies* 16, no. 1: 450.
https://doi.org/10.3390/en16010450