# Impact of Grid-Connected Inverter Parameters on the Supraharmonic Emissions in Distributed Power Generation Systems

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## Abstract

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## 1. Introduction

- Giving mathematical expressions that present the parameters that affect the SH emissions of GCIs;
- Studying the effect of some of the parameters on the emissions of GCIs mathematically by simulation and by experimental studies;
- Studying the effect of parameters’ symmetry and asymmetry of parallel-connected GCIs on the total emissions to the grid;
- Giving a corner stone for studying the propagations and penetration of SH emissions of GCIs in single-phase installations in addition to filtering them out and preventing them from flowing into the grid.

## 2. SH Emissions of Single-Phase GCI

## 3. GCI Parameter Effect on the High Frequency Emissions

## 4. Carrier Phase-Shift Concept to Reduce the Total SH Emissions of Parallel GCIs in DPGSs

## 5. Simulation Studies

#### 5.1. GCI Model

#### 5.2. Simulation with One GCI

- The amplitude of the SH emissions of single-phase GCIs depends on the DC-link voltage and the coupling filter inductance.
- The relationship between the DC-link voltage and SH emissions amplitudes of GCIs is non-linear.
- The amplitudes of the SH emissions of GCIs are in an inverse relationship with the coupling filter inductance.
- The amplitude of the SH emissions of single-phase GCIs are independent of the active power variation.
- The phase of the carrier harmonics is independent of the active power variations
- The active power variation affects only the phase of the sideband harmonics.

#### 5.3. Simulation with Two Parallel GCIs

## 6. Experimental Verifications

#### 6.1. System Description

#### 6.2. Study 1: One GCI

#### 6.3. Study 2: Two Parallel GCIs

## 7. Conclusions and Future Work

- The amplitude of the SH emissions of single-phase GCIs depends on the DC-link voltage and the coupling filter inductance.
- The amplitude of the SH emissions of single-phase GCIs is independent of the active power variation.
- The phase of the carrier harmonics is independent of the active power variations
- The active power variation affects only the phase of the sideband harmonics.

- Studying deeply the propagations and penetrations of SH of single-phase GCIs in low-voltage grids.
- Studying the interference between single-phase GCIs and any other switching converter, such as switched-mode power supplies and LED lamps, at any residential installation.
- Developing active filters to mitigate the emissions of GCIs in the SH range.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DPGS | Distributed power generation system |

GCI | Grid-connected inverters |

PCC | Point of common coupling |

SH | Supraharmonic |

PV | Photovoltaic |

PWM | Pulse width modulation |

HF | High frequency |

PR | Proportional resonance |

WTHD | Weighted total harmonic distortion |

## Variables

${\mathit{v}}_{\mathit{i}}$ | Inverter output voltage |

${\mathit{V}}_{\mathit{d}\mathit{c}}$ | DC-link voltage |

${\mathit{\omega}}_{\mathit{g}}$ | Grid angular frequency—reference signal angular frequency |

${\mathit{\theta}}_{\mathit{g}}$ | Grid phase—reference signal phase |

${\mathit{\omega}}_{\mathit{c}}$ | Carrier angular frequency |

${\mathit{\theta}}_{\mathit{c}}$ | Carrier phase |

$\mathit{M}$ | Modulation index |

$\mathit{J}$ | Bessel function of the first kind |

${\mathit{v}}_{\mathit{g}}$ | Instantaneous value of the grid voltage |

${\mathit{V}}_{\mathbf{a}\mathit{m}\mathit{p}}$ | The amplitude of the grid voltage |

$\mathit{\delta}$ | The load angle |

${\mathit{i}}_{\mathit{g}}$ | The instantaneous current injected to the grid |

${\mathit{i}}_{\mathit{g}\mathit{f}}$ | The instantaneous fundamental current |

${\mathit{i}}_{\mathit{g}\mathit{s}}$ | The instantaneous carrier switching harmonics |

${\mathit{i}}_{\mathit{g}\mathit{s}\mathit{b}}$ | The instantaneous sideband current switching harmonics |

${\mathit{L}}_{\mathit{f}}$ | The coupling filter inductance |

${\mathit{L}}_{\mathit{g}}$ | The grid inductance |

${\mathit{r}}_{\mathit{f}}$ | The coupling filter resistance |

${\mathit{r}}_{\mathit{g}}$ | The grid resistance |

RMS | Root mean square |

${\mathit{V}}_{1}$ | RMS values of fundamental |

${\mathit{V}}_{\mathit{k}}$ | RMS values of n-order harmonic components |

## Appendix A. Load Angle Definition in Power Systems

## References

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**Figure 1.**Single-phase GCI structure. Here, ${V}_{dc}$ is the DC-link voltage; ${S}_{1},{S}_{2},{S}_{3}$ and ${S}_{4}$ are the switches of the inverter; ${i}_{GCI}$ is the instantaneous value of the GCI current; ${L}_{f}$ is the coupling filter inductance, ${v}_{i}$ is the instantaneous value of the inverter output voltage between points A and B; ${r}_{g}$ and ${L}_{g}$ are the grid resistance and inductance, respectively; and ${v}_{g}$ is the instantaneous value of the grid voltage.

**Figure 2.**Sine-triangle modulation for driving the semiconductor switches of the single-phase GCI. Here, $M$ is the modulation index; ${\omega}_{g}$ is the reference signal angular frequency; ${\theta}_{g}$ is the control signal phase; ${\omega}_{c}$ is the carrier signal angular frequency.

**Figure 10.**GCIs and the total grid currents under symmetry scenario (

**a**) in time and (

**b**) in frequency.

**Figure 11.**GCIs and the total grid currents under asymmetry scenario (

**a**) in time and (

**b**) in frequency.

**Figure 16.**Effect of changing the coupling inductance on the amplitude of the chosen harmonic examples.

**Figure 18.**The results of two symmetric parallel-connected GCIs (

**a**) as a function of time and (

**b**) as a function of frequency.

**Figure 19.**The results of two asymmetric parallel-connected GCI (

**a**) as a function of time and (

**b**) as a function of frequency.

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

DC-link voltage | 600 V |

Switching frequency | 16 kHz |

Coupling filter inductance | $1\mathsf{\Omega}$, 10 mH |

Injected active power | 1.6263 kW |

Grid impedance | ${r}_{g}=0.01\mathsf{\Omega},{\mathrm{L}}_{\mathrm{g}}=0.1\mathrm{mH}$ |

Grid voltage and frequency | 230 V_{rms}, 50 Hz |

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**MDPI and ACS Style**

Aboutaleb, A.M.; Desmet, J.; Knockaert, J.
Impact of Grid-Connected Inverter Parameters on the Supraharmonic Emissions in Distributed Power Generation Systems. *Machines* **2023**, *11*, 1014.
https://doi.org/10.3390/machines11111014

**AMA Style**

Aboutaleb AM, Desmet J, Knockaert J.
Impact of Grid-Connected Inverter Parameters on the Supraharmonic Emissions in Distributed Power Generation Systems. *Machines*. 2023; 11(11):1014.
https://doi.org/10.3390/machines11111014

**Chicago/Turabian Style**

Aboutaleb, Abdellatif M., Jan Desmet, and Jos Knockaert.
2023. "Impact of Grid-Connected Inverter Parameters on the Supraharmonic Emissions in Distributed Power Generation Systems" *Machines* 11, no. 11: 1014.
https://doi.org/10.3390/machines11111014