# Model for Optimal Power Coefficient Tracking and Loss Reduction of the Wind Turbine Systems

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Literature Review

#### 1.2. Research Gap and Originality Highlights

## 2. Model Development

## 3. Results and Discussion

#### 3.1. Estimation of the Optimal Value of the Power Coefficient in a Direct Drive Configuration

#### 3.1.1. Power Loss Estimation Based on the Optimal Value of Cp

#### 3.1.2. Validation of the Model Results with the Experimental System

#### 3.2. Model Application to a Real Case Study in Pakistan Considering the Indirect Drive Configuration

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Comparison between the model results and measured data from the experimental setup in this study.

**Figure 8.**Geographical map of the wind power classification at a 50 m height in different areas in Pakistan [43].

**Figure 10.**Model results for a 20 kW indirect drive wind turbine installed in Gwadar city: (

**a**) wind speed, (

**b**) behavior of decision variables, (

**c**) generator torque and angular speed, and (

**d**) power losses.

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

Wind Turbine | ||

$\mathrm{Rated}\mathrm{power}({P}_{rated}$) | 100 W | [28] |

Blade length (L) | 0.58 m | [28] |

$\mathrm{Rated}\mathrm{wind}\mathrm{speed}({V}_{rat}$) | $11.4$m/s | [29] |

$\mathrm{Cut}-\mathrm{in}\mathrm{wind}\mathrm{speed}({V}_{Cin})$ | 2.8 m/s | [30] |

$\mathrm{Cut}-\mathrm{out}\mathrm{wind}\mathrm{speed}({V}_{Cout})$ | 25 m/s | [31] |

Aerodynamic Power Coefficients and Wind Regime Limits | ||

C_{1} | 0.5176 | [32] |

C_{2} | 116 | [33] |

C_{3} | 0.4 | [34] |

C_{4} | 5 | [23] |

C_{5} | −21 | [33] |

C_{6} | 0.0068 | [32] |

TSR Coefficients | ||

C_{7} | 1 | [34] |

C_{8} | 0.08 | [23] |

C_{9} | 1 | [32] |

C_{10} | 0.035 | [35] |

Copper Loss | ||

$\mathrm{Inlet}\mathrm{voltage}({V}_{i}$) | 24 V | [36] |

$\mathrm{Number}\mathrm{of}\mathrm{phases}(\mathrm{Q}$) | 3 | [37] |

Armature resistence (Ra) | 0.195 Ω | [38] |

Mechanical losses | ||

$\mathrm{Rotor}\mathrm{weight}({K}_{B})$ | 0.00005 | [22] |

IGBT Loss | ||

$\mathrm{Recovery}\mathrm{switching}\mathrm{energy}\left({k}_{rr}\right)$ | 655 mJ | [39] |

$D$ | 0.5 s | [39] |

$d$ | 0.00233675 | [38] |

$c$ | 2.19211 | [27] |

${k}_{ton}$ | 0.26 mJ | [39] |

${k}_{toff}$ | 3.45 mJ | [39] |

a | 1.09619 | [27] |

b | 0.00112801 | [38] |

$\mathrm{Collector}-\mathrm{to}-\mathrm{emitter}\mathrm{voltage}({V}_{CE}$) | 2.2 V | [27] |

Magnetic flux density (B) | $1.2\mathrm{Wb}/{\mathrm{m}}^{2}$ | [40] |

Induction Motor | |
---|---|

Torque type | 12:V/F control (variable) |

Rated power | 0.4 kW |

Number of poles | 4 |

Rated voltage | 200 V |

Rated current | 2.2 A |

Frequency | 50 Hz |

V/F control | 12A12 |

Power factor | 75.6 |

Rated rpm | 1410 |

Permanent Magnet Synchronous Generator | |

Item type | AC wind generator |

Model | NE-100S |

Number of phases | 3 |

Magnetic steel material | Neodymium |

Breaking method | Electromagnetic |

Brand | WolfGo |

Manufacturing country | China |

Tachometer | TI-900 (measuring range: 2.5 to 99,999 rpm) |

Clamp-on power meter | Hioki PW3360-20 |

Parameter. | Value | Reference |
---|---|---|

$\mathrm{Rated}\mathrm{power}({P}_{rat})$ | 20 kW | [47] |

Turbine swept area diameter (D) | 10.58 m | [47] |

Turbine blade radius (R) | 5.29 m | [47] |

Magnetic flux density of generator (B) | $0.82\mathrm{Wb}/{\mathrm{m}}^{2}$ | [48] |

$\mathrm{Armature}\mathrm{resistance}\mathrm{of}\mathrm{generator}({R}_{a}$) | 0.2873 Ω | [48] |

$\mathrm{Apparent}\mathrm{power}\mathrm{of}\mathrm{generator}(S)$ | 25 KVA | [49] |

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**MDPI and ACS Style**

Sohail, K.; Farzaneh, H.
Model for Optimal Power Coefficient Tracking and Loss Reduction of the Wind Turbine Systems. *Energies* **2022**, *15*, 4159.
https://doi.org/10.3390/en15114159

**AMA Style**

Sohail K, Farzaneh H.
Model for Optimal Power Coefficient Tracking and Loss Reduction of the Wind Turbine Systems. *Energies*. 2022; 15(11):4159.
https://doi.org/10.3390/en15114159

**Chicago/Turabian Style**

Sohail, Kashif, and Hooman Farzaneh.
2022. "Model for Optimal Power Coefficient Tracking and Loss Reduction of the Wind Turbine Systems" *Energies* 15, no. 11: 4159.
https://doi.org/10.3390/en15114159