Southern Taiwan University Department of Electrical engineering

1
Southern Taiwan UniversityDepartment of
Electrical engineering

• A statistical analysis of wind power density
• based on the Weibull and Rayleigh models at
• he southern region of Turkey
• 
  Author Ali Naci Celik
• (
  Received 21 April 2003
• 
  accepted 27 July 2003)
• 
  Present Bui Trong Diem

2
Information part

• Abstract
• Distributional parameters of the wind data used
• Wind speed probability distributions
• Power density distributions and mean power
  density
• Conclusions

3
ABSTRACT

• - Studies show that Iskenderun (360N 360E)
  located on the Mediterranean coast of Turkey.
• The wind energy potential of the region is
  statistically analyzed based on 1-year measured
  hourly time series wind speed data.
• Two probability density functions are ?tted to
  the measured probability distributions on a
  monthly basis.
• The wind energy potential of the location is
  studied based on the Weibull and the Rayleigh
  models.

4
Introduction

• -The electric generating capacity of Turkey as of
  1999 was 26226 Gwe
• As of 2000, electricity generation in turkey is
  mainly hydroelectric (40) and conventional
  thermal power plants (60, coal, natural, gas)
• The renew energy of Turkey will reach
  approximately 18500Mwe by the year 2010.
• The total installed wind power generation
  capacity of Turkey is 19.1Mwe in three wind power
  stations.

5
Distributional parameters of the wind data used

• - the monthly mean wind speed values and
  standard deviation calculator for the available
  times data using Eqs.1 and 2

d

• - Alternatively, the mean wind speed can be
  determined from

6
Distributional parameters of the wind data used
7
Wind speed probability distributions

• - The wind speed data in time-series format is
  usually arranged in the frequency distribution
  format since it is more convenient for
  statistical analysis.

8
Wind speed probability distributions

• Probability density function of the Weibull
  distribution is given by.

9
Wind speed probability distributions

• - The corresponding cumulative probability
  function of the Weibull distribution is,

10
Wind speed probability distributions
- v, the following is obtained for the mean wind
speed,
11
Wind speed probability distributions

• Note that the gamma function has the properties
  of

- The probability density and the cumulative
distribution functions of the Rayleigh model are
given by,
12
Wind speed probability distributions
- The correlation coefficient values are used
as the measure of the goodness of the ?t of the
probability density distributions obtained from
the Weibull and Rayleigh models.
13
Power density distributions and
mean power density

• - If the power of the wind per unit area is
  given by

• The referent mean wind power density determine by

• The most general equation to calculate the mean
  wind power density is,

• - The mean wind power density can be calculated
  directly from the following equation if the mean
  value of v3 s,( v3)m, is already known,

14
Power density distributions and mean power density

• From Eq. (3), the mean value of v3s can be
  determined as

• Integrating Eq. (13), the following is obtained
  for the Weibull function,

• Introducing Eqs. (6) and (14) into Eq. (12), the
  mean power density for the Weibull function
  becomes

15
Power density distributions and mean power density

• - For k 2, the following is obtained from Eq. (6)

- By extracting c from Eq. (16) and setting k
equal to 2, the power density for the Rayleigh
model is found to be,
- The minimum power densities occur in February
and November, with 7.54 and 9.77 W/m2,
respectively. It is interesting to note that the
highest power density values occur in the summer
months of June, July and August, with the maximum
value of 63.69 W/m2 in June.
16
Power density distributions and mean power density

• - The errors in calculating the power densities
  using the models in comparison to those using the
  measured probability density distributions are
  presented in Fig. 6, using the following formula

17
Power density distributions and mean power density

• The highest error value occurs in July with 11.4
  for the Weibull model. The power density is
  estimated by the Weibull model with a very small
  error value of 0.1 in April. The yearly average
  error value in calculating the power density
  using the Weibull function is 4.9, using the
  following equation

18
Power density distributions and mean power density
19
Conclusions

• Even though Iskenderun is shown as one of the
  most potential wind energy generation regions in
  Turkey. This is shown by the low monthly and
  yearly mean wind speed and power density values.
• As the yearly average wind power density value of
  30.20 W/m2 indicates,
• However, the diurnal variations of the seasonal
  wind speed and the wind powerdensity have to be
  further studied, since the diurnal variation may
  show a significant difference.

20
Conclusions

• - The Weibull model is better in ?tting the
  measured monthly probability density
  distributions than the Rayleigh model. This is
  shown from the monthly correlation efficiency
  values of the ?ts.
• - The Weibull model provided better power density
  estimations in all 12 months than the Rayleigh
  model.

21
Southern Taiwan UniversityDepartment of
Electrical engineering

• Thank you very much