# Adaptive Fuzzy Approximation Control of PV Grid-Connected Inverters

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## Abstract

**:**

## 1. Introduction

_{∞}robust control technique. Additionally, adaptive control techniques and model predictive controllers for grid-connected and standalone inverters were reported in [15,16,17,18]. In all studies referred to, the proposed non-linear controllers showed better performance when compared with linear controllers’ performance. The main drawback of nonlinear control methods is that they rely on the system mathematical model and system parameters availability.

- The paper proposes an adaptive fuzzy approximation control scheme for GCIS.
- Excellent tracking performance of the proposed controller is obtained under different operating conditions such as power factor, parameter, and modelling uncertainties.

## 2. Grid-Connected Inverter System (GCIS)

#### 2.1. GCIS Description

#### 2.2. MIMO Model of GCIS

#### 2.3. Input-Output Feedback Linearization of GCIS

## 3. The Proposed Controller

#### 3.1. Adaptive Fuzzy Approximation Controller for GCIS

#### 3.2. Closed-Loop Stability

**Theorem**

**1.**

**Proof.**

## 4. Implementation of the Proposed Adaptive Fuzzy Controller for GCIS

## 5. Simulation Cases and Results

#### 5.1. Case I: Unity Power Factor Tracking

#### 5.2. Case II: Tracking of Power Factor Changes

#### 5.3. Case III: Robust Tracking

#### 5.4. Case IV: Tracking in the Presence of Model Uncertainity

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AFC | Adaptive fuzzy control |

DG | Distributed generation |

FLC | Fuzzy logic controllers |

GCIS | Grid-connected inverter systems |

IC | Incremental conductance |

IT2FLC | Interval Type-2 fuzzy logic controller |

LQG | Linear Quadratic Gaussian |

MIMO | Multi-input multi-output |

PI | Proportional-integral |

PR | Proportional resonant |

P&O | Perturb and observe |

PV | Photovoltaic |

PWM | Pulse width-modulation |

RC | Repetitive controller |

RES | Renewable energy sources |

SVPWM | Space vector pulse width modulation |

T2FLC | Type-2 fuzzy logic controller |

THD | Total harmonic distortion |

TSKPFNN | Takagi–Sugeno–Kang-type probabilistic fuzzy neural network |

VSI | Voltage source inverter |

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**Figure 2.**The proposed adaptive fuzzy control (AFC) technique for the grid connected inverter system (GCIS).

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

Grid Voltage rms | 120 V |

Inductance L Resistor R | 2 mH 0.1 Ω |

Grid Frequency | 50 Hz |

DC link capacitor | 2200 µF |

PV array voltage Vdc | 540 V |

PV array current Ipv | 3.46 A |

$\mathbf{State}\downarrow $ | $\mathbf{Fuzzy}\mathbf{Set}\to $ | N | Z | P |
---|---|---|---|---|

${x}_{1}$ | ${\overline{x}}_{1}^{N}=-5\phantom{\rule{0ex}{0ex}}{\sigma}_{1}^{N}=6$ | ${\overline{x}}_{1}^{Z}=0\phantom{\rule{0ex}{0ex}}{\sigma}_{1}^{Z}=6$ | ${\overline{x}}_{1}^{P}=5\phantom{\rule{0ex}{0ex}}{\sigma}_{1}^{P}=6$ | |

${x}_{2}$ | ${\overline{x}}_{2}^{N}=-0.1\phantom{\rule{0ex}{0ex}}{\sigma}_{2}^{N}=0.005$ | ${\overline{x}}_{2}^{Z}=0\phantom{\rule{0ex}{0ex}}{\sigma}_{2}^{Z}=0.005$ | ${\overline{x}}_{2}^{P}=0.1\phantom{\rule{0ex}{0ex}}{\sigma}_{2}^{P}=0.005$ | |

${x}_{3}$ | ${\overline{x}}_{3}^{N}=525\phantom{\rule{0ex}{0ex}}{\sigma}_{3}^{N}=100$ | ${\overline{x}}_{3}^{Z}=550\phantom{\rule{0ex}{0ex}}{\sigma}_{3}^{Z}=100$ | ${\overline{x}}_{3}^{P}=575\phantom{\rule{0ex}{0ex}}{\sigma}_{3}^{P}=100$ |

**Table 3.**Comparison between the performance of the proposed controller, PI, and TSKPFNN controllers.

Controller | Max Overshoot % | Settling Time (S) |
---|---|---|

PI controller | 75 | 0.04 |

TSKPFNN controller | 12.24 | 0.3 |

Proposed AFC | 0.0 | 0.035 |

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**MDPI and ACS Style**

Shadoul, M.; Yousef, H.; Al Abri, R.; Al-Hinai, A.
Adaptive Fuzzy Approximation Control of PV Grid-Connected Inverters. *Energies* **2021**, *14*, 942.
https://doi.org/10.3390/en14040942

**AMA Style**

Shadoul M, Yousef H, Al Abri R, Al-Hinai A.
Adaptive Fuzzy Approximation Control of PV Grid-Connected Inverters. *Energies*. 2021; 14(4):942.
https://doi.org/10.3390/en14040942

**Chicago/Turabian Style**

Shadoul, Myada, Hassan Yousef, Rashid Al Abri, and Amer Al-Hinai.
2021. "Adaptive Fuzzy Approximation Control of PV Grid-Connected Inverters" *Energies* 14, no. 4: 942.
https://doi.org/10.3390/en14040942