# Model Predictive Virtual Flux Control Method for Low Switching Loss Performance in Three-Phase AC/DC Pulse-width-Modulated Converters

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## Abstract

**:**

## 1. Introduction

- -
- A power loss reduction is achieved without deteriorating the input current’s harmonic distortion and the DC output’s voltage ripple.
- -
- The sinusoidal input current is maintained under distorted source voltage conditions thanks to the use of virtual flux.
- -
- The proposed technique allows for the straightforward implementation of the voltage vector preselection strategy even in practical systems.
- -
- The requirements of additional terms in the cost function and extra hardware to implement the proposed approach are eliminated.

## 2. Conventional Model Predictive Control Approaches for AC/DC Converter

## 3. Proposed High Efficiency Model Predictive Virtual Flux Control with Voltage Vector Preselection Strategy for AC/DC Converter

## 4. Evaluation Results

- Case 1. This is an ideal condition where the AC source voltages are perfectly balanced and sinusoidal.
- Case 2. This is a distorted source voltage condition where the fifth harmonic component is injected to phase-a AC source voltage.

#### 4.1. Simulation Results Analysis

#### 4.2. Experimental Results

#### 4.3. Performance Evaluation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Conventional MPCC for AC/DC converter [18].

**Figure 3.**Conventional MPVFC for AC/DC converter [19].

**Figure 5.**Proposed high-efficiency MPVFC with voltage vector preselection strategy for AC/DC converter (“*” stands for reference).

**Figure 6.**Simulation waveforms under ideal conditions. (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC.

**Figure 7.**Simulation waveforms under distorted source voltage conditions (10% fifth harmonic injection in phase-a). (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC.

**Figure 8.**Simulation waveforms under ideal conditions with periodical change in reference DC output voltage. (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC ((

**i**) entire simulation duration; (

**ii**) a part of simulation duration).

**Figure 9.**Simulation waveforms under ideal conditions with periodical change in load resistance. (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC ((

**i**) entire simulation duration; (

**ii**) a part of simulation duration).

**Figure 11.**Experimental waveforms under ideal conditions. (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC ((

**i**) input currents and phase-a AC source voltage, (

**ii**) FFT analysis of input current, (

**iii**) DC output voltage and switching signals).

**Figure 12.**Experimental waveforms under distorted source voltage conditions (10% fifth harmonic injection in phase-a). (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC ((

**i**) input currents and phase-a AC source voltage, (

**ii**) FFT analysis of input current, (

**iii**) DC output voltage and switching signals).

**Figure 13.**Experimental waveforms under ideal conditions with step change in reference DC output voltage. (

**a**) Conventional MPCC, (

**b**) conventional MPVFC, (

**c**) proposed MPVFC.

**Figure 14.**Performance of AC/DC converter obtained using proposed MPVFC method under ideal condition with uncertainty of filter inductance. (

**a**) Model inductance is 50% smaller than actual inductance. (

**b**) Model inductance is 50% higher than actual inductance.

**Figure 15.**Performance of AC/DC converter obtained using proposed MPVFC method under distorted source voltage condition (10% fifth harmonic injection in phase-a) with uncertainty of filter inductance. (

**a**) Model inductance is 50% smaller than actual inductance. (

**b**) Model inductance is 50% higher than actual inductance.

**Figure 16.**Performance comparison between conventional MPCC, conventional MPVFC, and proposed MPVFC methods under varied sampling periods. (

**a**) Input current average THD, (

**b**) DC output voltage peak-to-peak ripple, (

**c**) total switching loss, (

**d**) efficiency.

**Figure 17.**Performance comparison between conventional MPCC, conventional MPVFC, and proposed MPVFC methods under variation of magnitude of injected fifth harmonic component. (

**a**) Input current average THD, (

**b**) DC output voltage peak-to-peak ripple, (

**c**) total switching loss, (

**d**) efficiency.

**Figure 18.**Performance of proposed MPVFC method under variation in filter inductance uncertainty. (

**a**) Input current average THD, (

**b**) DC output voltage peak-to-peak ripple, (

**c**) total switching loss, (

**d**) efficiency.

AC/DC Converter Input Voltage Vector | Magnitude | ${\mathit{S}}_{\mathit{a}}$ | ${\mathit{S}}_{\mathit{b}}$ | ${\mathit{S}}_{\mathit{c}}$ |
---|---|---|---|---|

${V}_{0}$ | 0 | 0 | 0 | 0 |

${V}_{1}$ | $\frac{2}{3}{V}_{dc}{e}^{j0}$ | 1 | 0 | 0 |

${V}_{2}$ | $\frac{2}{3}{V}_{dc}{e}^{j\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ | 1 | 1 | 0 |

${V}_{3}$ | $\frac{2}{3}{V}_{dc}{e}^{j\raisebox{1ex}{$2\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ | 0 | 1 | 0 |

${V}_{4}$ | $\frac{2}{3}{V}_{dc}{e}^{j\pi}$ | 0 | 1 | 1 |

${V}_{5}$ | $\frac{2}{3}{V}_{dc}{e}^{j\raisebox{1ex}{$4\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ | 0 | 0 | 1 |

${V}_{6}$ | $\frac{2}{3}{V}_{dc}{e}^{j\raisebox{1ex}{$5\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ | 1 | 0 | 1 |

${V}_{7}$ | 0 | 1 | 1 | 1 |

**Table 2.**Preselected voltage vectors following reference AC/DC converter input voltages and input currents (“*” stands for reference).

Reference AC/DC Converter Input Voltage | Input Currents | Clamping Phase | Preselected Voltage Vectors | |
---|---|---|---|---|

${\mathit{v}}_{\mathbf{C}\mathbf{O}\mathbf{N}\mathbf{V},\mathit{m}\mathit{a}\mathit{x}}^{\mathit{*}}$ | ${\mathit{v}}_{\mathbf{C}\mathbf{O}\mathbf{N}\mathbf{V},\mathit{m}\mathit{i}\mathit{n}}^{\mathit{*}}$ | |||

${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}a}^{*}$ | ${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}b}^{*}$ | $\left|{i}_{sa}\right|>\left|{i}_{sb}\right|$ | Phase-$a$ | ${V}_{1},{V}_{2},{V}_{6},{V}_{7}$ |

$\left|{i}_{sa}\right|<\left|{i}_{sb}\right|$ | Phase-$b$ | ${V}_{0},{V}_{1},{V}_{5},{V}_{6}$ | ||

${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}c}^{*}$ | $\left|{i}_{sa}\right|>\left|{i}_{sc}\right|$ | Phase-$a$ | ${V}_{1},{V}_{2},{V}_{6},{V}_{7}$ | |

$\left|{i}_{sa}\right|<\left|{i}_{sc}\right|$ | Phase-$c$ | ${V}_{0},{V}_{1},{V}_{2},{V}_{3}$ | ||

${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}b}^{*}$ | ${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}a}^{*}$ | $\left|{i}_{sb}\right|>\left|{i}_{sa}\right|$ | Phase-$b$ | ${V}_{2},{V}_{3},{V}_{4},{V}_{7}$ |

$\left|{i}_{sb}\right|<\left|{i}_{sa}\right|$ | Phase-$a$ | ${V}_{0},{V}_{3},{V}_{4},{V}_{5}$ | ||

${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}c}^{*}$ | $\left|{i}_{sb}\right|>\left|{i}_{sc}\right|$ | Phase-$b$ | ${V}_{2},{V}_{3},{V}_{4},{V}_{7}$ | |

$\left|{i}_{sb}\right|<\left|{i}_{sc}\right|$ | Phase-$c$ | ${V}_{0},{V}_{1},{V}_{2},{V}_{3}$ | ||

${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}c}^{*}$ | ${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}a}^{*}$ | $\left|{i}_{sc}\right|>\left|{i}_{sa}\right|$ | Phase-$c$ | ${V}_{4},{V}_{5},{V}_{6},{V}_{7}$ |

$\left|{i}_{sc}\right|<\left|{i}_{sa}\right|$ | Phase-$a$ | ${V}_{0},{V}_{3},{V}_{4},{V}_{5}$ | ||

${v}_{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{V}b}^{*}$ | $\left|{i}_{sc}\right|>\left|{i}_{sb}\right|$ | Phase-$c$ | ${V}_{4},{V}_{5},{V}_{6},{V}_{7}$ | |

$\left|{i}_{sc}\right|<\left|{i}_{sb}\right|$ | Phase-$b$ | ${V}_{0},{V}_{1},{V}_{5},{V}_{6}$ |

Parameter | Value |
---|---|

AC source voltage ${v}_{s}$ (${V}_{peak}$) | 120 V |

Filter resistance ${R}_{s}$ | 0.1 Ω |

Filter inductance ${L}_{s}$ | 15 mH |

DC-link output capacitance ${C}_{dc}$ | 550 µF |

Load resistance ${R}_{L}$ | 100 Ω |

Fundamental frequency $f$ | 60 Hz |

Sampling period ${T}_{sp}$ | 50 µs |

Reference DC output voltage ${V}_{dc,ref}$ | 300 V |

P gain ${k}_{p}$ | 0.1 |

I gain ${k}_{i}$ | 5 |

Parameter | Value |
---|---|

${r}_{T}$ | 7.3 mΩ |

${V}_{T}$ | 1.45 V |

${r}_{D}$ | 6.7 mΩ |

${V}_{F}$ | 1.37 V |

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**MDPI and ACS Style**

Nguyen, M.H.; Kwak, S.; Choi, S.
Model Predictive Virtual Flux Control Method for Low Switching Loss Performance in Three-Phase AC/DC Pulse-width-Modulated Converters. *Machines* **2024**, *12*, 66.
https://doi.org/10.3390/machines12010066

**AMA Style**

Nguyen MH, Kwak S, Choi S.
Model Predictive Virtual Flux Control Method for Low Switching Loss Performance in Three-Phase AC/DC Pulse-width-Modulated Converters. *Machines*. 2024; 12(1):66.
https://doi.org/10.3390/machines12010066

**Chicago/Turabian Style**

Nguyen, Minh Hoang, Sangshin Kwak, and Seungdeog Choi.
2024. "Model Predictive Virtual Flux Control Method for Low Switching Loss Performance in Three-Phase AC/DC Pulse-width-Modulated Converters" *Machines* 12, no. 1: 66.
https://doi.org/10.3390/machines12010066