### Abstract

The relevance of the discussed issue is caused by the imperfection of existing methodology of predicting the characteristics of wind turbines. The main aim of the study is to improve the existing methodology of calculating the performance of the high-power wind turbine, parametric analysis, comparing the results with those given by other authors. Methods. In the improved methodology of calculation using Pearson s chi-squared test the statistical hypothesis on the distribution of the general totality of air velocities by Weibull Gnedenko is tested. The distribution parameters are found by numerical solution of the transcendental equation with the definition of the gamma function interpolation formula. The values of the operating characteristic of the incomplete gamma function are defined by numerical integration using Weddle s rule. The methodology is automated for Turbo Pascal. Results. The paper introduces the results of calculating the characteristics of the high-power wind turbine, found by using the improved parts of the methodology connecting with testing the statistical hypothesis on the distribution of the general totality of air velocities by Weibull Gnedenko, the exact calculations of the values of the gamma function and incomplete gamma function. The comparison of the calculated results using the proposed methodology with those obtained by other authors found significant differences in the values of the sample variance and empirical Pearson. The authors have analyzed the initial and maximum wind speed influence on performance of the wind turbine. Conclusions. The Weibull Gnedenko function can be used to describe wind characteristics in the areas with moderate and strong winds. Varying the wind speed in the range of possible rates does not affect the average value of the operating characteristic and performance of the wind turbine. Increasing the maximum wind speed leads to a significant increase in these parameters. The improved methodology of calculating the performance of high-power wind turbines can be used in the design organizations and educational process.

Original language | English |
---|---|

Pages (from-to) | 17-22 |

Number of pages | 6 |

Journal | Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering |

Volume | 326 |

Issue number | 8 |

Publication status | Published - 1 Jan 2015 |

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### Keywords

- Air density
- Average efficiency
- Distribution function of the Weibull Gnedenko
- Electrical power
- Gamma function
- Operating characteristic
- Pearson s chis-quared test
- Sample variance
- Standard height of a weather vane
- Wind speed
- Wind turbine

### ASJC Scopus subject areas

- Materials Science (miscellaneous)
- Fuel Technology
- Geotechnical Engineering and Engineering Geology
- Waste Management and Disposal
- Economic Geology
- Management, Monitoring, Policy and Law

### Cite this

**Calculating the performance of high<power wind turbine by the improved methodology.** / Goldaev, Sergey V.; Radyuk, Karina N.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Calculating the performance of high<power wind turbine by the improved methodology

AU - Goldaev, Sergey V.

AU - Radyuk, Karina N.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The relevance of the discussed issue is caused by the imperfection of existing methodology of predicting the characteristics of wind turbines. The main aim of the study is to improve the existing methodology of calculating the performance of the high-power wind turbine, parametric analysis, comparing the results with those given by other authors. Methods. In the improved methodology of calculation using Pearson s chi-squared test the statistical hypothesis on the distribution of the general totality of air velocities by Weibull Gnedenko is tested. The distribution parameters are found by numerical solution of the transcendental equation with the definition of the gamma function interpolation formula. The values of the operating characteristic of the incomplete gamma function are defined by numerical integration using Weddle s rule. The methodology is automated for Turbo Pascal. Results. The paper introduces the results of calculating the characteristics of the high-power wind turbine, found by using the improved parts of the methodology connecting with testing the statistical hypothesis on the distribution of the general totality of air velocities by Weibull Gnedenko, the exact calculations of the values of the gamma function and incomplete gamma function. The comparison of the calculated results using the proposed methodology with those obtained by other authors found significant differences in the values of the sample variance and empirical Pearson. The authors have analyzed the initial and maximum wind speed influence on performance of the wind turbine. Conclusions. The Weibull Gnedenko function can be used to describe wind characteristics in the areas with moderate and strong winds. Varying the wind speed in the range of possible rates does not affect the average value of the operating characteristic and performance of the wind turbine. Increasing the maximum wind speed leads to a significant increase in these parameters. The improved methodology of calculating the performance of high-power wind turbines can be used in the design organizations and educational process.

AB - The relevance of the discussed issue is caused by the imperfection of existing methodology of predicting the characteristics of wind turbines. The main aim of the study is to improve the existing methodology of calculating the performance of the high-power wind turbine, parametric analysis, comparing the results with those given by other authors. Methods. In the improved methodology of calculation using Pearson s chi-squared test the statistical hypothesis on the distribution of the general totality of air velocities by Weibull Gnedenko is tested. The distribution parameters are found by numerical solution of the transcendental equation with the definition of the gamma function interpolation formula. The values of the operating characteristic of the incomplete gamma function are defined by numerical integration using Weddle s rule. The methodology is automated for Turbo Pascal. Results. The paper introduces the results of calculating the characteristics of the high-power wind turbine, found by using the improved parts of the methodology connecting with testing the statistical hypothesis on the distribution of the general totality of air velocities by Weibull Gnedenko, the exact calculations of the values of the gamma function and incomplete gamma function. The comparison of the calculated results using the proposed methodology with those obtained by other authors found significant differences in the values of the sample variance and empirical Pearson. The authors have analyzed the initial and maximum wind speed influence on performance of the wind turbine. Conclusions. The Weibull Gnedenko function can be used to describe wind characteristics in the areas with moderate and strong winds. Varying the wind speed in the range of possible rates does not affect the average value of the operating characteristic and performance of the wind turbine. Increasing the maximum wind speed leads to a significant increase in these parameters. The improved methodology of calculating the performance of high-power wind turbines can be used in the design organizations and educational process.

KW - Air density

KW - Average efficiency

KW - Distribution function of the Weibull Gnedenko

KW - Electrical power

KW - Gamma function

KW - Operating characteristic

KW - Pearson s chis-quared test

KW - Sample variance

KW - Standard height of a weather vane

KW - Wind speed

KW - Wind turbine

UR - http://www.scopus.com/inward/record.url?scp=85018900566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018900566&partnerID=8YFLogxK

M3 - Article

VL - 326

SP - 17

EP - 22

JO - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

JF - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

SN - 2500-1019

IS - 8

ER -