Southern Taiwan UniversityDepartment of Electrical engineering

A statistical analysis of wind power densitybased 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

Information partAbstractDistributional parameters of the wind data usedWind speed probability distributionsPower density distributions and mean power

densityConclusions

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 fitted 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.

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.

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

Distributional parameters of the wind data used

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.

Wind speed probability distributions

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

Wind speed probability distributions

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

Wind speed probability distributions

- v, the following is obtained for the mean wind speed,

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,

Wind speed probability distributions

- The correlation coefficient values are used as the measure of the goodness of the fit of the probability density distributions obtained from the Weibull and Rayleigh models.

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,

Power density distributions and mean power density

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

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

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

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.

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:

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

Power density distributions and mean power density

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.

- The Weibull model is better in fitting the measured monthly probability density distributions than the Rayleigh model. This is shown from the monthly correlation efficiency values of the fits.

- The Weibull model provided better power density estimations in all 12 months than the Rayleigh model.

Conclusions

Southern Taiwan University

Department of Electrical engineering

Thank you very much