# A Robust Interval Type-2 Fuzzy Logic Controller for Variable Speed Wind Turbines Based on a Doubly Fed Induction Generator

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions and avoiding the high cost of energy production induced by the conventional energy sources [1]. Therefore, the use of renewable energies is the only way to reduce the dependence on fossil fuel energies (coal, oil, natural gas, etc.) that generate carbon dioxide (CO

_{2}) and other polluting gases. Among the renewable energy sources are solar energy, hydropower, and wind energy [2].

_{2}) [3].

## 2. WEC System Model

#### 2.1. Modeling of the Wind Turbine

^{3}), ($R$) presents the turbine blades’ radius, ($\lambda $) is the speed ratio, (${V}_{w}$) is the speed of wind (m/s), while (${C}_{p}$) presents the power coefficient that depends on the pitch angle ($\beta $). The parameters $\lambda $ and ${C}_{p}$ can be expressed as described in the following equations:

#### 2.2. Modeling of DFIG

#### 2.3. Description of Fuzzy Logic SETs

#### 2.3.1. Overview of Type-1 Fuzzy Logic Sets (T1-FLS)

#### 2.3.2. Basic Concepts of Interval Type-2 Fuzzy Logic Sets (IT2-FLS)

#### 2.3.3. Control of Doubly Fed Induction Generator Using IT2-FL

- -
- The fuzzifier stage is used to translate inputs (real values) to fuzzy values.
- -
- The inference (reasoning) stage consists of two blocks, the rules base and the inference engine; it works the same way as for type-1 fuzzy systems, except the antecedents’ fuzzy sets and the consequent are represented by type-2 fuzzy sets.
- -
- The process consists of combining the rules base to produce a mapping from input to the output type-2 fuzzy set [23]. It is necessary to calculate the intersection, union and composition of type-2 relations in order to realize this mapping.
- -
- The type reducer is used to convert all type-2 fuzzy sets into a type-1 fuzzy set on the output. There are several methods to calculate the reduced set, such as joint center, center of sums, height, and center joint, among others [24].
- -
- The defuzzification stage translates an output into precise values.

## 3. Simulation Results

#### 3.1. Reference Tracking

- -
- Case 1: The wind turbine operated in the MPPT operating mode when the speed of wind was lower than the rated speed ${V}_{n}=12\mathrm{m}/\mathrm{s}$, therefore the wind turbine could generate the maximum power according to the specific wind speed.
- -
- Case 2: In high wind speeds, the pitch control started operating. Therefore, the pitch angle was increased in order to limit the captured wind energy to its nominal value.

#### 3.2. Robustness

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Wind energy conversion system (WECS) based on a direct drive dual field induction generator (DFIG); (

**b**) curves of the power coefficient $({C}_{p})$ as a function of $\lambda $ and $\beta $.

**Figure 4.**Structures of fuzzy logic control: (

**a**) type-1 fuzzy logic controller (T1-FLC); (

**b**) interval type-2 fuzzy logic controller (IT2-FLC).

**Figure 5.**Type-1 fuzzy membership functions (MFs): (

**a**) MFs for input variable ‘e’ and ‘de’ of the T1-FLC; (

**b**) MFs for output variable ‘u’ of the T1-FLC.

**Figure 6.**Type-2 fuzzy membership functions (MFs): (

**a**) MFs for input variable ‘e’ and ‘de’ of the IT2-FLC; (

**b**) MFs for output variable ‘u’ of the IT2-FLC.

**Figure 11.**(

**a**) Active power (${P}_{s}$) comparison under normal conditions; (

**b**) reactive power (${Q}_{s}$ ) comparison under normal conditions.

**Figure 12.**Rotor current response comparison under normal conditions; (

**a**) rotor current (${I}_{qr}$); (

**b**) rotor current (${I}_{dr}$ ).

**Figure 13.**(

**a**) Rotor currents ${I}_{ra}$, ${I}_{rb}$, and ${I}_{rc}$; (

**b**) Stator currents ${I}_{sa}$ and stator voltage ${V}_{sa}$.

**Figure 14.**(

**a**) Active power tracking comparison under parameters variation; (

**b**) reactive power tracking comparison under parameters variation.

Error | $\int \mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$ | ||||||
---|---|---|---|---|---|---|---|

NB | NM | NS | EZ | PS | PM | PB | |

NB | NB | NB | NB | NB | NM | NS | EZ |

NM | NB | NB | NB | NM | NS | EZ | PS |

NS | NB | NB | NM | NS | EZ | PS | PM |

EZ | NB | NM | NS | EZ | PS | PM | PB |

PS | NM | NS | EZ | PS | PM | PB | PB |

PM | NS | EZ | PS | PM | PB | PB | PB |

PB | EZ | PS | PM | PB | PB | PB | PB |

Parameters | Values |
---|---|

Radius of the blades | $45\mathrm{m}$ |

Gear ratio | $100$ |

Total Inertia | $254\mathrm{Kg}.{\mathrm{m}}^{2}$ |

Friction coefficient | $0.24$ |

Parameters | Values |
---|---|

Rated power | $3\mathrm{MW}$ |

Frequency | $50\mathrm{Hz}$ |

Stator voltage | $690\mathrm{V}$ |

Stator inductance | $12.241\text{}\mathrm{mH}$ |

Stator resistance | $2.97\text{}\mathrm{m}\Omega $ |

Rotor resistance | $3.82\text{}\mathrm{m}\Omega $ |

Rotor inductance | $12.177\text{}\mathrm{mH}$ |

Mutual inductance | $12.12\text{}\mathrm{mH}$ |

Number of pole pairs | $2$ |

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**MDPI and ACS Style**

Hemeyine, A.V.; Abbou, A.; Bakouri, A.; Mokhlis, M.; El Moustapha, S.M.o.M.
A Robust Interval Type-2 Fuzzy Logic Controller for Variable Speed Wind Turbines Based on a Doubly Fed Induction Generator. *Inventions* **2021**, *6*, 21.
https://doi.org/10.3390/inventions6020021

**AMA Style**

Hemeyine AV, Abbou A, Bakouri A, Mokhlis M, El Moustapha SMoM.
A Robust Interval Type-2 Fuzzy Logic Controller for Variable Speed Wind Turbines Based on a Doubly Fed Induction Generator. *Inventions*. 2021; 6(2):21.
https://doi.org/10.3390/inventions6020021

**Chicago/Turabian Style**

Hemeyine, Ahmed Vall, Ahmed Abbou, Anass Bakouri, Mohcine Mokhlis, and Sidi Mohamed ould Mohamed El Moustapha.
2021. "A Robust Interval Type-2 Fuzzy Logic Controller for Variable Speed Wind Turbines Based on a Doubly Fed Induction Generator" *Inventions* 6, no. 2: 21.
https://doi.org/10.3390/inventions6020021