Conflict of interest

The authors certify that this work has no conflict of interest with any organization or entity in the subject matter or materials discussed in this chapter.

and pressure (Figure 7(a and b)), despite the commonly used Weibull distribution for mean wind speed. The bi-lognormal and bi-gamma distributions are best fit for temperature and humidity ratio, respectively. The existence of bimodal shape of the distributions of temperature is likely related to the very distinguished high and low temperature corresponding to the summer and winter seasons, respectively, in Ithaca. The same reason explains the bimodal shape for humidity. The obtained specific distributions for the meteorological parameters, provided in Table 2, are readily applicable for WT performance analyses, i.e., fatigue, structure, aerodynamics, and thermodynamics, in moderately complex terrain of the northeastern United States. Figure 7(e) presents the empirical cumulative distribution function (CDF) of energy and exergy efficiencies calculated herein. Due to the large amount of 0 energy and exergy efficiencies when wind speed is below the cut-in wind speed, the CDF curves show that there is a probability of �43% that the efficiencies are equal to 0. The largest discrepancy between CDF of energy and exergy efficiencies occurs at efficiencies equal to 0.4. The presented CDF could be used to evaluate the reliability of wind power performance considering realistic

Probability density function

exp ð Þz ½ � <sup>1</sup> <sup>þ</sup> exp ð Þ<sup>z</sup> <sup>2</sup> ,

exp ð Þz ½ � <sup>1</sup> <sup>þ</sup> exp ð Þ<sup>z</sup> <sup>2</sup> ,

<sup>b</sup> , a <sup>¼</sup> <sup>1</sup>:2307, b <sup>¼</sup> <sup>0</sup>:<sup>2887</sup>

<sup>b</sup> , a <sup>¼</sup> <sup>11</sup>:4812, b <sup>¼</sup> <sup>0</sup>:<sup>0041</sup>

<sup>þ</sup> ð Þ <sup>1</sup> � <sup>w</sup> <sup>1</sup> xb<sup>2</sup> ffiffiffiffiffi

w ¼ 0:5824, a<sup>1</sup> ¼ 5:6125, b<sup>1</sup> ¼ 0:0280, a<sup>2</sup> ¼ 5:6752, b<sup>2</sup> ¼ 0:0182

w ¼ 0:5970, a<sup>1</sup> ¼ 3:8190, b<sup>1</sup> ¼ 0:0010, a<sup>2</sup> ¼ 12:6287, b<sup>2</sup> ¼ 0:0008

<sup>2</sup><sup>π</sup> <sup>p</sup> exp �ð Þ ln <sup>x</sup> � <sup>a</sup><sup>1</sup> <sup>2</sup> 2b<sup>2</sup> 1 " #

<sup>x</sup><sup>a</sup>1�<sup>1</sup> exp � <sup>x</sup>

<sup>2</sup><sup>π</sup> <sup>p</sup> exp �ð Þ ln <sup>x</sup> � <sup>a</sup><sup>2</sup> <sup>2</sup> 2b<sup>2</sup> 2 " #

> b1 � �

> > b2 � � ,

<sup>x</sup><sup>a</sup>2�<sup>1</sup> exp � <sup>x</sup>

,

xb<sup>1</sup> ffiffiffiffiffi

ba1 <sup>1</sup> Γð Þ a<sup>1</sup>

<sup>þ</sup> ð Þ <sup>1</sup> � <sup>w</sup> <sup>1</sup> ba2 <sup>2</sup> Γð Þ a<sup>2</sup>

b 1 x

b 1 x

where <sup>z</sup> <sup>¼</sup> ln ð Þ� <sup>x</sup> <sup>a</sup>

distribution f x<sup>ð</sup> <sup>j</sup>w; <sup>a</sup>1; <sup>b</sup>1; <sup>a</sup>2; <sup>b</sup>2Þ ¼ <sup>w</sup> <sup>1</sup>

distribution f x<sup>ð</sup> <sup>j</sup>w; <sup>a</sup>1; <sup>b</sup>1; <sup>a</sup>2; <sup>b</sup>2Þ ¼ <sup>w</sup> <sup>1</sup>

The best-fit distribution form and distribution parameters for the four meteorological variables.

where <sup>z</sup> <sup>¼</sup> ln ð Þ� <sup>x</sup> <sup>a</sup>

This chapter presents methods and results for thermodynamic analysis of wind energy systems considering four types of meteorological variables, i.e., wind speed, pressure, temperature, and humidity. An improved understanding of WT efficiencies is critically important and necessary before launching any wind projects. The evaluation of WT efficiencies considering thermodynamics, conducted here for an

meteorological uncertainty.

5. Conclusions

16

Meteorological variables

Wind speed (ms�<sup>1</sup> )

Temperature (K)

Humidity ratio (kg kg�<sup>1</sup> )

Table 2.

Pressure (Pa) Log-logistic

Best-fit distribution type

Wind Solar Hybrid Renewable Energy System

Log-logistic

Bi-lognormal

Bi-gamma

The distributional fits and empirical histograms are shown in Figure 7.

distribution f xð Þ¼ <sup>j</sup>a; <sup>b</sup> <sup>1</sup>

distribution f xð Þ¼ <sup>j</sup>a; <sup>b</sup> <sup>1</sup>
