Wind Speed Extrapolation (Power Law) :-) hi is the height the wind speed is measured h is the height the wind speed is extrapolated Vi is the wind speed at height h Vzis the wind speed at height ha a is the roughness value Landscape type Friction coefficienta Lakes, ocean and smooth hard ground 0.10 Grasslands (ground level) 0.15 Tall crops, hedges and shrubs 0.20 Heavily forested land Small town with some trees and shrubs 0.30 City areas with high rise buildings 0.25 11.40 4) Design a wind turbine with a rotor radius of 25 meters, use your optimum wind speed and finally estimate the power output? (takec, as 0.4, p = 1.225 kg/m) Wind Power Equation p=xpxAxvx where, P is the power in Watts, p is the air density in kg/m", A is the rotor area in m, V is the wind speed in m's, Ce is the power coefficient Betz limit says that no wind turbine can convert more than 59.3% of the kinetic energy of the wind into mechanical energy turning a rotor, i.e cpme=0.593. Extrapolate the wind speed to 100 meters of height (which is the height of the tower), please also note that the region you study is a grassland or a heavily forested land depending on your group number. Son Mģ) Your wind speed data corresponds to 10 meters of height from the ground.
Do not forget to add 4 different constraints to indicate the minimum and the maximum values of the coordinates. X2 -1 Give the screen shot of your solver parameters as attached to your word file. Indicate the optimum location on the map below.
Determine the optimum location and the maximum speed at this location. What do you think about the accuracy of the model (check R), and is there any insignificant variable (check the p value of each variable)?Ģ) Now you know the wind speed as a function of coordinates: Optimize the function by using Excel Solver. 1) Fit a multiple polynomial regression in the form of: f(x,x)= B.+BX+B.x2 +B,x+B.x2? To do this create two new columns x, and xz in excel (an example is given below), use "analysis toolpak” to fit a regression.
For this purpose, you have collected the average wind speed data at 10 meters elevation from the ground (measured through years) corresponding to different coordinates (in km) of a proper geographical region.
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