# Power Quality Enhancement of Grid-Connected Renewable Systems Using a Matrix-Pencil-Based Active Power Filter

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure of SAPF

## 3. The DC Link

_{ref}represents the DC voltage reference value and V

_{dc}represents the capacitor instantaneous voltage value. The difference between these two values represents the error, which serves as the input to the PI controller. The active power exchange between the grid and the DC link is caused by current I

_{loss}, which reflects the fundamental frequency of the active current. The transfer function of this outer loop PI controller is presented in [30].

## 4. Integrating the loss current in MPM formulation

#### 4.1. Signal Model

#### 4.2. The Matrix Pencil Method

## 5. Simulation Results and Discussion

^{−6}s. For the PWM and SVPWM, the switching frequency is set to 12.5 kHz, while for the hysteresis control, the hysteresis band is set to 0.1 A. The circuit parameters used in the simulation scenarios are given in Table 1.

#### 5.1. Battery DC Link

_{L}, the compensation current I

_{h}, and the source current I

_{s,}using the three extraction methods and PWM control. The results reveal the effectiveness of MPM in compensating source current harmonics to obtain a nearly sinusoidal source current. Figure 9c, depicting the waveform when using MPM, reveals a smoother source current waveform than that of the IRPT and SRF, which agrees with the results in Table 2.

#### 5.2. Capacitor DC Link

_{dc}is used in the DC link with the value given in Table 1. A PI controller is used for the outer control loop to set the capacitor voltage at a specified reference value. IRPT, SRF, and MPM are tested using hysteresis, PWM, and SVPWM to check the performance of these extraction methods in mitigating the source current harmonics. The source current THDs are summarized in Table 3.

#### 5.3. Dynamic Response under Capacitor DC Link

_{L}= 20 Ω, L

_{L}= 1 mH) in parallel to non-linear load 1. The waveform of the source current and its FFT analyzer with no filter for this load condition are depicted in Figure 13 with a THD of 23.22%.

#### 5.4. Power Factor Correction under Capacitor DC Link

_{L}= 5 Ω, L

_{L}= 20 mH) is added in parallel to the non-linear load 1. The waveform of the source current and its FFT analyzer with no filter are reflected in Figure 16 with a THD of 7.47%. This value is lower than that of load 1 and load 2 with no filter due to its highly inductive property. The power factor of load 1 with no filter is 0.9961, whereas the PF when load 3 is added to load 1 is 0.8147.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Battery DC link FFT analyzer for source current with PWM control using (

**a**) IRPT extraction technique, (

**b**) SRF extraction technique, and (

**c**) MPM extraction technique.

**Figure 9.**Battery DC link waveforms of I

_{L}, I

_{h}, and I

_{s}for SAPF with PWM control using (

**a**) IRPT extraction, (

**b**) SRF extraction, and (

**c**) MPM extraction.

**Figure 10.**Capacitor DC link FFT analyzer for SAPF with SVPWM control using (

**a**) IRPT extraction (

**b**) SRF extraction (

**c**) MPM extraction.

**Figure 11.**Capacitor DC link Waveforms of I

_{L}, I

_{h}, and I

_{s}for SAPF with SVPWM control using (

**a**) IRPT extraction, (

**b**) SRF extraction, and (

**c**) MPM extraction.

**Figure 12.**DC-link capacitor’s voltage when using SVPWM control with (

**a**) IRPT extraction, (

**b**) SRF extraction, and (

**c**) MPM extraction.

**Figure 13.**FFT analyzer with no filter with the addition of load 2. (

**a**) Source current waveform. (

**b**) FFT window.

**Figure 14.**Capacitor DC link FFT analyzer for SAPF with hysteresis control while adding load 2 using (

**a**) IRPT extraction, (

**b**) SRF extraction, and (

**c**) MPM extraction.

**Figure 15.**Capacitor DC link waveforms of I

_{L}, I

_{h}, I

_{s}, DC-link capacitor’s voltage value for SAPF with hysteresis control while adding load 2 using (

**a**) IRPT extraction, (

**b**) SRF extraction, and (

**c**) MPM extraction.

**Figure 16.**Capacitor DC link FFT analyzer with no filter with the addition of load 3. (

**a**) Source current waveform. (

**b**) FFT window.

**Figure 17.**Capacitor DC link FFT analyzer for SAPF with PWM control while adding load 3 using (

**a**) IRPT extraction, (

**b**) SRF extraction, and (

**c**) MPM extraction.

Circuit Parameters | Parameter Value |
---|---|

Frequency | 50 Hz |

Supply phase voltage peak value | 220 V |

Source impedance (R_{s}, L_{s}) | 0.15 Ω, 0.03 mH |

Line impedance (R_{r}, L_{r}) | 1 Ω, 1 mH |

Coupling reactance | 3 mH |

DC-link capacitance (C_{dc}) | 3000 µF |

DC-link voltage reference (V_{ref}) | 700 V |

Load 1 impedance (R_{L}, L_{L}) | 40 Ω, 2 mH |

Extraction Technique | % THD of Source Current | ||
---|---|---|---|

Hysteresis | PWM | SVPWM | |

IRPT | 1.74% | 1.24% | 1.39% |

SRF | 1.46% | 1.26% | 1.41% |

MPM | 1.22% | 0.83% | 0.93% |

Extraction Technique | % THD of Source Current | ||
---|---|---|---|

Hysteresis | PWM | SVPWM | |

IRPT | 1.74% | 1.21% | 1.37% |

SRF | 1.61% | 1.43% | 1.54% |

MPM | 1.21% | 0.85% | 0.93% |

Extraction Technique | % THD of Source Current | ||
---|---|---|---|

Hysteresis | PWM | SVPWM | |

IRPT | 1.04% | 0.85% | 0.88% |

SRF | 1.51% | 1.52% | 1.61% |

MPM | 0.64% | 0.52% | 0.55% |

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**MDPI and ACS Style**

Chahine, K.; Tarnini, M.; Moubayed, N.; El Ghaly, A.
Power Quality Enhancement of Grid-Connected Renewable Systems Using a Matrix-Pencil-Based Active Power Filter. *Sustainability* **2023**, *15*, 887.
https://doi.org/10.3390/su15010887

**AMA Style**

Chahine K, Tarnini M, Moubayed N, El Ghaly A.
Power Quality Enhancement of Grid-Connected Renewable Systems Using a Matrix-Pencil-Based Active Power Filter. *Sustainability*. 2023; 15(1):887.
https://doi.org/10.3390/su15010887

**Chicago/Turabian Style**

Chahine, Khaled, Mohamad Tarnini, Nazih Moubayed, and Abdallah El Ghaly.
2023. "Power Quality Enhancement of Grid-Connected Renewable Systems Using a Matrix-Pencil-Based Active Power Filter" *Sustainability* 15, no. 1: 887.
https://doi.org/10.3390/su15010887