# Development of Various Types of Independent Phase Based Pulsewidth Modulation Techniques for Three-Phase Voltage Source Inverters

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## Abstract

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## 1. Introduction

## 2. Three-Phase DPWM Techniques

## 3. Per-Phase DPWM Technique for Independent Control of Switching Loss

## 4. Verification and Evaluation Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

2L3P | 2-level 3-phase |

VSI | Voltage source inverter |

THD | Total harmonic distortion |

CPWM | Continuous pulse-width-modulation |

DPWM | Discontinuous pulse-width-modulation |

SPWM | Sinusoidal pulse-width-modulation |

SVPWM | Space vector pulse-width-modulation |

CBPWM | Carrier-based pulse-width modulation |

GDPWM | Generalized discontinuous pulse-width-modulation |

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**Figure 3.**Modulation voltages and zero-sequence voltage signal waveforms obtained by different DPWM strategies (

**a**) DPWM0, (

**b**) DPWM1, (

**c**) DPWM2, (

**d**) DPWM3, (

**e**) DPWMMIN, (

**f**) DPWMMAX.

**Figure 4.**Modulation voltages, zero-sequence voltage signal waveforms, and phase output current waveforms obtained by GDPWM with (

**a**) load angle $\phi ={20}^{\mathrm{o}}$, (

**b**) load angle $\phi ={70}^{\mathrm{o}}$.

**Figure 6.**Flowchart of zero-sequence voltage generation in modified DPWM for independent control of per-phase switching loss.

**Figure 7.**Zero-sequence voltage, modulation voltages, and switching patterns waveforms obtained by various DPWM for independent control of per-phase switching loss (

**a**) Per-phase DPWM0, (

**b**) Per-phase DPWM1, (

**c**) Per-phase DPWM2, (

**d**) Per-phase DPWM3, (

**e**) Per-phase DPWMMIN, (

**f**) Per-phase DPWMMAX $({V}_{dc}=200\mathrm{V},\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={20}^{\mathrm{o}})$.

**Figure 8.**(

**a**) Flowchart of zero-sequence voltage generation in modified GDPWM for independent control of per-phase switching loss, (

**b**) Output currents, zero-sequence voltage signal, modulation voltages, and corresponding switching patterns waveforms obtained by per-phase GDPWM $({V}_{dc}=200\mathrm{V},\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={20}^{\mathrm{o}})$.

**Figure 10.**The simulation waveforms of output currents, modulation voltage, zero-sequence voltage, and switching patterns obtained by different Per-phase DPWM strategies (

**a**) Per-phase DPWM0, (

**b**) Per-phase DPWM1, (

**c**) Per-phase DPWM2, (

**d**) Per-phase DPWM3, (

**e**) Per-phase DPWMMIN, (

**f**) Per-phase DPWMMAX, (

**g**) Per-phase GDPWM.

**Figure 11.**Comparison results of conventional SVPWM and various per-phase DPWM strategies (

**a**) Average output current THD, (

**b**) Switching frequency of phase $a$, (

**c**) Power loss in phase $a$, (

**d**) Total loss, (

**e**) Efficiency. $({V}_{dc}=200\mathrm{V},\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}=0.87,\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={20}^{\mathrm{o}})$.

**Figure 12.**Comparison results of conventional SVPWM and various per-phase DPWM strategies (

**a**) Average output current THD, (

**b**) Switching frequency of phase $a$, (

**c**) Power loss in phase $a$, (

**d**) Total loss, (

**e**) Efficiency. $({V}_{dc}=200\mathrm{V},\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}=0.42,\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={75}^{\mathrm{o}})$.

**Figure 13.**Comparison results of the conventional SVPWM and various per-phase DPWM strategies under variation of carrier frequency (

**a**) Switching frequency of phase $a$, (

**b**) Average switching frequency, (

**c**) Average output current THD, (

**d**) Conduction loss in phase $a$, (

**e**) Switching loss in phase $a$, (

**f**) Total loss. $({V}_{dc}=200\mathrm{V},\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}{f}_{cr}=10\mathrm{k}\mathrm{H}\mathrm{z},\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={20}^{\mathrm{o}})$.

**Figure 14.**Comparison results of the conventional SVPWM and various per-phase DPWM strategies under variation of modulation index (

**a**) Switching frequency of phase $a$, (

**b**) Average switching frequency, (

**c**) Average output current THD, (

**d**) Conduction loss in phase $a$, (

**e**) Switching loss in phase $a$, (

**f**) Total loss. $({V}_{dc}=200\mathrm{V},\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}{f}_{cr}=10\mathrm{k}\mathrm{H}\mathrm{z},\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={20}^{\mathrm{o}})$.

**Figure 15.**Comparison results of the conventional SVPWM and various per-phase DPWM strategies under variation of load angle (

**a**) Switching frequency of phase $a$, (

**b**) Average switching frequency, (

**c**) Average output current THD, (

**d**) Conduction loss in phase $a$, (

**e**) Switching loss in phase $a$, (

**f**) Total loss. $({V}_{dc}=200\mathrm{V},\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}{f}_{cr}=10\mathrm{k}\mathrm{H}\mathrm{z},\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\phi ={20}^{\mathrm{o}})$.

**Figure 17.**The experimental waveforms of output currents, phase $a$ modulation voltage, and zero-sequence voltage signal obtained by different per-phase DPWM strategies (

**a**) Per-phase DPWM0, (

**b**) Per-phase DPWM1, (

**c**) Per-phase DPWM2, (

**d**) Per-phase DPWM3, (

**e**) Per-phase DPWMMIN, (

**f**) Per-phase DPWMMAX, (

**g**) Per-phase GDPWM.

**Figure 18.**The experimental waveforms of output currents, modulation voltage, and switching pattern of phase $a$ obtained by different Per-phase DPWM strategies (

**a**) Per-phase DPWM0, (

**b**) Per-phase DPWM1, (

**c**) Per-phase DPWM2, (

**d**) Per-phase DPWM3, (

**e**) Per-phase DPWMMIN, (

**f**) Per-phase DPWMMAX, (

**g**) Per-phase GDPWM.

**Figure 19.**Comparison results of conventional SVPWM and various per-phase DPWM strategies in terms of output current THD obtained from experimental results.

**Figure 20.**The simulation waveforms of output currents, modulation voltage, zero-sequence voltage, and switching patterns under unbalanced load condition $({R}_{a}=R,{R}_{b}=2R,{R}_{c}=0.5R)$ obtained by different Per-phase DPWM strategies (

**a**) Per-phase DPWM0, (

**b**) Per-phase DPWM1, (

**c**) Per-phase DPWM2, (

**d**) Per-phase DPWM3, (

**e**) Per-phase DPWMMIN, (

**f**) Per-phase DPWMMAX, (

**g**) Per-phase GDPWM.

$\mathit{\alpha}$ | $\mathit{\delta}$ | |
---|---|---|

SVPWM | 0.5 | x |

DPWM0 | $1-0.5\left\{1+sign\left[cos3(\omega t+\delta )\right]\}\right.$ | $\phi +{30}^{\mathrm{o}}$ |

DPWM1 | $1-0.5\left\{1+sign\left[cos3(\omega t+\delta )\right]\}\right.$ | $\phi $ |

DPWM2 | $1-0.5\left\{1+sign\left[cos3(\omega t+\delta )\right]\}\right.$ | $\phi -{30}^{\mathrm{o}}$ |

DPWM3 | $1-0.5\left\{1+sign\left[cos3(\omega t+\delta )\right]\}\right.$ | $\phi -{60}^{\mathrm{o}}$ |

DPWMMIN | 1 | x |

DPWMMAX | 0 | x |

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

$\mathrm{dc}\text{-}\mathrm{link}\mathrm{voltage}{V}_{dc}$ (V) | 200 |

dc-link capacitance (μF) | 680 |

$\mathrm{Load}\mathrm{resistance}R$ (Ω) | 10 |

$\mathrm{Load}\mathrm{inductance}{L}_{f}$ (mH) | 10 |

Carrier frequency (kHz) | 10 |

Fundamental frequency (Hz) | 60 |

P gain | 5 |

I gain | 100 |

Sampling frequency (kHz) | 10 |

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## Share and Cite

**MDPI and ACS Style**

Nguyen, M.H.; Kwak, S.; Choi, S.
Development of Various Types of Independent Phase Based Pulsewidth Modulation Techniques for Three-Phase Voltage Source Inverters. *Machines* **2023**, *11*, 1054.
https://doi.org/10.3390/machines11121054

**AMA Style**

Nguyen MH, Kwak S, Choi S.
Development of Various Types of Independent Phase Based Pulsewidth Modulation Techniques for Three-Phase Voltage Source Inverters. *Machines*. 2023; 11(12):1054.
https://doi.org/10.3390/machines11121054

**Chicago/Turabian Style**

Nguyen, Minh Hoang, Sangshin Kwak, and Seungdeog Choi.
2023. "Development of Various Types of Independent Phase Based Pulsewidth Modulation Techniques for Three-Phase Voltage Source Inverters" *Machines* 11, no. 12: 1054.
https://doi.org/10.3390/machines11121054