Report on Wind data analysis

Introduction of Wind data analysis

Wind data analysis is a technique to measure, predict and corelate the wind data sets. The climate reports are also considered to summarize the expected values for the average wind conditions with the different measurement points. There are different parameters to be calculated in the wind data analysis such as analysis of turbulence, shear and other meteorological parameters. In the present analysis annual percentage frequency for the different cities is considered. The main objective is to measure site parameters, plot Weibul distribution, maximum velocity, maximum energy availability, and capacity factors. The report include data for the efficient turbine to get nearly year-round power. The report is based on annual percentage frequency of wind speed groups and monthly mean wind speed for different stations.

Analysis based on annual percentage frequency

Table 1: Annual Percentage Frequency of Wind Speed Groups

St.No University Freq uency Percentage

Number 0-3  m/s 4-7  m/s 8-12  m/s 13-18  m/s 19-24 m/s 25-31 m/s 32-38 m/s 

1 441100116 7 18 35 29 9 2 0

2 441105868 4 9 18 27 21 14 5

Site parameters of Wind data analysis

Site parameters include mean energy density and height of the hub. The selection of the wind turbine model is dependent on the mean energy output and capacity factor. It is based on the cumulative distribution function for the mean wind speed and height of the hub. Average wind velocity is represented as equation 1 below, 

v_rmc   =   (1/n  ∑_(i =  1)^n▒v_i^3 )^(1/3)

Variance σ^2 of the data is defined

σ^2   =  1/(n -1 ) ∑_(i =  1)^n▒(v_i  -  v^' )_ ^2 

skewness  =((1 )/(n-1 ) ∑_(i =1)^n▒(v_i    -   v) ^3)/σ^3 

Kurtosis =  ( (1 )/(n-1 ) ∑_(i =1)^n▒(v_i    -   v) ^4)/σ^( 4)    -  3 

  k  =(σ/V_m )^( -  1.06)

c =   V_m/( γ (1+1/k) )

V_p  =  c ((k-1)/k)^(1/k)

V_( m)  =  c (k+2/k)^(1/k)

Number 0-3  m/s 4-7  m/s 8-12  m/s 13-18  m/s 19-24 m/s 25-31 m/s 32-38 m/s 

Average 5.5 13.5 26.5 28 15 8 2.5

Variance 2.25 20.25 72.25 1 36 36 6.25

SD 2.12132 6.363961 12.02082 1.414214 8.485281 8.485281 3.535534

Skewness #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Kurtosis #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

k 2.8141 2.263051 2.359591 25.59495 1.856537 0.938046 0.686342

V_p 4.705486 10.43319 20.97856 27.95644 9.888536 #NUM! #NUM!

V_M 6.65614 17.85923 34.37442 28.08243 22.23849 27.01918 18.25525

Plot Weibull distribution of Wind data analysis

probability density function =   f (v)  =  k/c  (v/c)^(k - 1)  exp⁡( -(v/c)^k )  

cumulative density function =  e^( -(v_x/c)^k )

Number 0-3  m/s 4-7  m/s 8-12  m/s 13-18  m/s 19-24 m/s 25-31 m/s 32-38 m/s 

f (v) 0.093255 0.022889 8.16E-06 2.33E-36 0.001629 0.001771 0.031568

Cumulative density function 0.31625 0.033555 0.001607 0.400875 0.011612 0.014681 0.17981

C_f 8.558871 5.787805 54.70476 1.31E+11 9.925713 #NUM! #NUM!

Figure 1: probability density function

Maximum velocity

Maximum energy availability of Wind data analysis

The maximum energy is a significant parameter for the wind energy assessment. The speed is calculated by using the equation below, 

V_M  =  c  ((k +  2)/k)^(( 1)/( k))

0-3  m/s 4-7  m/s 8-12  m/s 13-18  m/s 19-24 m/s 25-31 m/s 32-38 m/s 

V_M 6.65614 17.85923 34.37442 28.08243 22.23849 27.01918 18.25525

Capacity factor of Wind data analysis

CF of a wind turbine is estimated by using the following expressions on the basis of Weibull distribution function becomes,

P_(e avg)  =   P_rated    ((e^( (-V_c/c)^t  )  -  e^(- (v_rated/c)^k ))/((v_rated/c)^k-  (V_(c )/c)^k )  -   e^(- (V_c/c)^k )  )

C_f  =    P_(e avg)/P_rated 

0-3  m/s 4-7  m/s 8-12  m/s 13-18  m/s 19-24 m/s 25-31 m/s 32-38 m/s 

C_f 8.558871 5.787805 54.70476 1.31E+11 9.925713 #NUM! #NUM!

Monthly mean in different cities of Wind data analysis

Table 2: Monthly Mean Wind Speed For Different Stations

St.No University Monthly Mean Speeds

Number Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1 441100116 7 7.8 7.2 7 7 8 7.3 7 8.8 9.1 6.3 7

2 441105868 4.1 4.3 4.8 5.2 5.3 5.8 5.5 5.9 5.2 4.3 4 4.3

Site parameters of Wind data analysis

c =   V_m/( γ (1+1/k) )

V_p  =  c ((k-1)/k)^(1/k)

V_( m)  =  c (k+2/k)^(1/k)

Number Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Average 5.55 6.05 6 6.1 6.15 6.9 6.4 6.45 7 6.7 5.15 5.65

Variance 2.1025 3.0625 1.44 0.81 0.7225 1.21 0.81 0.3025 3.24 5.76 1.3225 1.8225

SD 2.05061 2.474874 1.697056 1.272792 1.202082 1.555635 1.272792 0.777817 2.545584 3.394113 1.626346 1.909188

Skewness #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Kurtosis #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

k 2.948474 2.639902 3.941142 5.484052 5.887218 5.041716 5.777564 9.946921 2.999793 2.0929 3.496596 3.248799

V_p 4.822558 5.051618 5.570577 5.880132 5.958573 6.603976 6.192899 6.38166 6.114936 4.911943 4.677 5.045098

V_M 6.615473 7.490865 6.658535 6.455845 6.46323 7.372741 6.737904 6.569902 8.299592 9.231055 5.861246 6.549013

Plot Weibull distribution of Wind data analysis

Maximum velocity

Maximum energy availability

Capacity factor