﻿ Calculation of Wind power density：WPD by RETSCREEN® ENGINEERING & CASES TEXTBOOK

# Calculation of Wind power density：WPD by RETSCREEN® ENGINEERING & CASES TEXTBOOK

 1 Average wind speed value：x_avg m/s 0＜x_avg 2 Shape factor：k 1＜k 3 Air density：ρ kg/m^3 - 4 a,b a：,b： If enpty, 0 and 25 are set respectively. 5 Graph x-axis:x_avg,y-axis：p(x) x-axis:k,y-axis：p(x) x-axis:ρ,y-axis：p(x) Plot Input Data： YesNo 6 Number of gridlines of Graph x-axis, y-axis -
:Export Graph Image.

## Keyword

Wind power density WPD,Wind speed distribution, Gamma function, Weibull probability density function

## Reference

[1]：I.N.ブロンシュテイン・ K.A.セメンジャーエフ・ G.グロッシェ：『数学ハンドブック』.pp.121-122.
[2]：大野豊・磯田和男：『新版数値計算ハンドブック』.pp.955-956.
[3]：RETScreen® International『CLEAN ENERGY PROJECT ANALYSIS：RETSCREEN® ENGINEERING & CASES TEXTBOOK　WIND ENERGY PROJECT ANALYSIS CHAPTER』.pp.13-28.

## Remarks

・Γ(x+1)≈1+b1*x+b2*x^2+b3*x^3+b4*x^4+b5*x^5+b6*x^6+b7*x^7+b8*x^8.(Approximation of Hastings.Reference[2])
b1=-0.577191652
b2=0.988205891
b3=-0.897056937
b4=0.918206857
b5=-0.756704078
b6=0.482199394
b7=-0.193527818
b8=0.035868343
・Γ(1+x)=x*Γ(x).
・Γ(x)*Γ(-x)=-π/(x*sin(π*x)).(Reference[1])
・『The shape factor will typically range from 1 to 3. For a given average wind speed, a lower shape factor indicates a relatively wide distribution of wind speeds around the average while a higher shape factor indicates a relatively narrow distribution of wind speeds around the average. A lower shape factor will normally lead to a higher energy production for a given average wind speed.』(Reference[3])
・『The Weibull probability density function expresses the probability p(x) to have a wind speed x during the year』(Reference[3])