# Development and Application of Fuzzy Proportional-Integral Control Scheme in Pitch Angle Compensation Loop for Wind Turbines

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## Abstract

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## 1. Introduction

- The combination of the control of rotor speed and output power using fuzzy tuned PI in power control, allowing the changeable tuning of PI parameters depending on system conditions;
- Regulating the output power while maintaining the desired rotor speed and avoiding equipment overloads;
- For power levels below a nominal value, the power is controlled to reduce the turbine speed according to the power–speed curve (tracking curve) illustrated in [31]. This is approximated by adjusting the reference speed.

## 2. Wind Turbine Aerodynamics

_{t}from kinetic energy of the wind and is given by:

_{v}is the wind speed, and Cp is the power coefficient, which is a function of tip speed ratio λ (TSR) and the blade pitch angle [34]. TSR is a function of the angular speed of the rotor Ω

_{m}and is given by:

_{e}that is a function of the stator flux φ and rotor current i

_{r}and i

_{s}given by the following equation:

_{s}, L

_{m}are stator and magnetizing inductance. P is the number of pole pairs. d and q subscripts refer to the d-q axis components in the synchronous frame [36].

## 3. Pitch Angle Control

## 4. Fuzzy Logic Approach

## 5. Designing and Applying Fuzzy PI in Pitch Angle Control

- IF e is P and Δe is P THEN dkp is NB.
- IF e is Z and Δe is P THEN dkp is Z.
- IF e is N and Δe is N THEN dkp is PB.

## 6. Model Configuration and Results Discussion

#### 6.1. Ramp Wind Speed

#### 6.2. Step Wind Speed

#### 6.3. Random Wind Speed

#### 6.4. Extreme Wind Speed

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 10.**System response during ramp wind speed: (

**a**) wind speed, (

**b**) pitch angle, (

**c**) active power of first row, (

**d**) total active power, (

**e**) rotor speed.

**Figure 11.**System response during step wind speed: (

**a**) wind speed, (

**b**) pitch angle, (

**c**) active power of first row, (

**d**) total active power, (

**e**) rotor speed.

**Figure 12.**System response during random wind speed: (

**a**) wind speed, (

**b**) pitch angle, (

**c**) active power of first row, (

**d**) total active power, (

**e**) rotor speed.

**Figure 13.**System response during extreme wind speed: (

**a**) wind speed, (

**b**) pitch angle, (

**c**) active power of first row, (

**d**) total active power, (

**e**) rotor speed.

dkp | Derivative of Error | |||
---|---|---|---|---|

P | Z | N | ||

Error | P | NB | NM | NS |

Z | Z | Z | Z | |

N | PS | PM | PB |

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**MDPI and ACS Style**

AlGhamdi, S.; Hamdan, I.; Youssef, M.M.M.; Noureldeen, O.
Development and Application of Fuzzy Proportional-Integral Control Scheme in Pitch Angle Compensation Loop for Wind Turbines. *Machines* **2021**, *9*, 135.
https://doi.org/10.3390/machines9070135

**AMA Style**

AlGhamdi S, Hamdan I, Youssef MMM, Noureldeen O.
Development and Application of Fuzzy Proportional-Integral Control Scheme in Pitch Angle Compensation Loop for Wind Turbines. *Machines*. 2021; 9(7):135.
https://doi.org/10.3390/machines9070135

**Chicago/Turabian Style**

AlGhamdi, S., I. Hamdan, Marwa M. M. Youssef, and Omar Noureldeen.
2021. "Development and Application of Fuzzy Proportional-Integral Control Scheme in Pitch Angle Compensation Loop for Wind Turbines" *Machines* 9, no. 7: 135.
https://doi.org/10.3390/machines9070135