VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum,

EG0700565 Assessment of Wind Speed and Wind Power through Three Stations in Egypt, Including Air Density Variation and Analysis Results with Rough Set Theory

Khaled S. M. Essa1, M. Embaby1, A. M. Koza2, M. E. Abd El-Monsef2 and A. A. Marrouf1 1Mathematics and Theoretical Physics Department, NRC, AEA, Cairo, Egypt. 2Mathematics Department, Faculty of Science, Tanta University

ABSTRACT

It is well known that the wind energy potential is proportional to both air density and the third power of the wind speed average over a suitable time period. The wind speed and air density have random variables depending on both time and location. The main objective of this work is to derive the most general wind energy potential of the wind formulation putting into consideration the time variable in both wind speed and air density. The correction factors derived explicitly in terms of the cross-correlation and the coefficients of variation. The application is performed for environmental and wind speed measurements at the Cairo Airport, Kosseir and Hurguada, Egypt. Comparisons are made between Weibull, Rayleigh, and actual data distributions of wind speed and wind power of one year 2005. A Weibull distribution is the best match to the actual probability distribution of wind speed data for most stations. The maximum wind energy potential was 373 W/m2 in June while the annual mean value was 207 W/m2 at Hurguada (Red Sea coast). By using Rough set Theory, the wind power was found to depend on the wind speed greater than air density.

Kew Words: Potential energy of the wind/ air density/ wind speed

INTRODUCTION

As a result of increasing air pollution in the lower atmospheric layers due to different kinds of fuel products, man looked for alternative, renewable, clean and less expensive energy resources. The wind energy as well as the solar energy is the best of all kinds of energy that avoid production of air pollutions. In this work we shall deal with obtaining the wind energy at Cairo Airport, Kosseir and Hurguada sites. Evidently all the wind energy investigated depends on the average wind speed cube and probability distribution function (PDF) [1, 2]. Moreover, Auwera et al. [3] showed that a three- parameter Weibull distribution fits the wind speed data in a more refined manner than the two- parameter Weibull (PDF). Explicit formulation of wind energy in terms of absolute temperature, pressure and wind speed has been presented already by Sen and Sahin [4].

In this work we shall take into account some random variables in both air density and wind speed, which were assumed as constant in many practical applications. A new formulation of the wind energy potential, calculations is presented which accounts for the cross random properties of wind speed and air density time series. We considered measurements at Cairo Airport, Kosseir and Hurguada, Egypt, as an example.

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

Historically, Ancient used wind energy in windmills for grinding grain and pumping water from the river for irrigation. However, the utilization of windmills declined abruptly due to the use of oil fuelled diesel engines water pumping. Yet wind turbine technology has now been developed so the cost of electricity generated by wind has decreased substantially due to the reduction in the installed cost of turbines and the greater efficiency in energy production per installed kilowatt, due to improvements in reliability and availability of the plant [5]. Comparison of the cost estimates for electricity generated from fossil fuels, nuclear energy, and wind show that wind energy may be the cheapest source of electricity [6].

Egypt is one of the most rapidly developing nations in the with a population of about 72 million. The rural and remote areas are about 90% of the total habituated area. The main source of energy in Egypt is petroleum products. Despite the discovery of oil that makes Egypt an oil exporting country, the large national consumption for such a large population makes it very difficult to satisfy energy needs. Assessment of the advanced technologies [7] indicates that wind power, photovoltaic and, solar thermal power, solar heating and cooling and biomass energy systems are all viable options for developing nations. Egypt possesses a very good potential of solar and wind energies [8] consequently, a comprehensive assessment of resources and the corresponding economics for their applications must be carried out.

At the end of 20th century, a new way appeared, this is know as Rough set theory approach, this doesn’t depend on external suppositions. It is known as (let data speak) [9]. This is good for all types of data. The theory was originated by Pawlak in 1982 [10] as a result of long term program of fundamental research on logical properties of information systems, carried out by him and a group of logicians from Phlish Academy of sciences and the university of Warsaw, Poland.

Various real life application of rough sets have shown its usefulness in many domains as civil engineering [11], medical data analysis [12,13,14], generating of a cement kiln control algorithm from observation of stocker’s actions [15], vibration analysis [16], air craft pilot performance evaluation [17], hydrology [18], pharmacology [19], image processing [20] and ecology.

The basic information needed to evaluate mean wind power density is the wind speed probability distribution. Therefore this statistical study has to be carried out for the predictability of wind speed through the year at Cairo Airport, Kosseir and Hurguada -Egypt.

RANDOM STRUCTURE OF WIND ENERGY

The average air density ρ =1.225 kg/m3 at sea level and at temperature 150C.The wind energy potential ,E, of an air flow through a unit surface area perpendicular to the air stream during a unit time is given as: 1 P = ρV 3 (1) 2 Where V is the wind speed and the unit of energy is W/m2 (watt per meter square) provided that V is in m/s. In the derivation, one of the basic assumptions is that the air density is constant at its average level and the wind speed is at the instantaneous value. Consequently, both air density and wind speed are independent. However, practically none of these assumptions is valid exactly. The application of Eq.(1) is impossible over a finite time duration. Primitive thoughts of application with finite time series in the form of air density and wind speed records lead to average wind energy, Ē as: 1 P = ρV 3 2

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

3 Where ρ and V are the arithmetic averages of the air density and wind speed cube, respectively. In statistical terminology this expression can be rewritten in terms of the expectation operation as: 1 E(P) = E(ρ)E( V 3 ) (2) 2 Where E( ) represents the expectation of the argument, which is equivalent to the arithmetic, averages of a long time series[9].

At high-altitude stations, the sea level density assumption causes available wind energy to be overestimated by nearly 30% due to the variations in air density according to Reed [22]. He proposed an air density correction factor in order to convert the sea-level wind energy estimates to the site altitude. This density correction factor is dependent on the site elevation and the annual cycle of monthly mean temperatures.

In addition to the wind speed, the air density shows statistical variations with time. Hence, in any wind energy potential calculations joint random behaviors must be considered for a better wind energy formulation. THE CORRECTION FACTOR:

In view of the theory of dependent random variables [9], if air density and wind speed are dependent on each other then the expectation of both sides in Eq. (1) leads by definition to: 1 E()P = E(ρ V 3 ) (3) 2 In general the multiplication of two dependent random variables can be written in terms of the expectations of their multiplication and the multiplication of their individual expectations by random covariance defined as: Cov(ρ , V 3 ) = E(ρ V 3 ) − E(ρ)E(V 3 ) (4) The cross correlation coefficient, r, between the wind speed cube and the air density is defined as: Cov(ρ ,V 3 ) r = (5) S S ρ V 3 where Sρ and S are the standard deviation of air density and wind speed cube time series, V 3 respectively. The elimination of Cov (ρ,V3) between equations (4) and (5) yields: E(ρ V 3) = E(ρ)E(V 3) + rS S (6) ρ V 3 Substituting into Eq.(3) yields: 1 ⎡ 3 ⎤ E()P = ⎢E(ρ)E(V ) + rS S ⎥ (7) 2 ⎣ ρ V 3 ⎦

It is to be noted that this expression can be reduced to some simple approaches that are available in experimental applications as follows: (1) In the above equation, the second term makes the major difference from the formulations presented in the literatures. Obviously, this term vanishes in case of constant air density because r = 0. In this case Eq.(7) is reduced to Eq.(2). This means that E ( ρ ) = ρ , consequently: 1 E()P = ρ E (V 3 ) (8) 2

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

(2) There is no cross-correlation for instantaneous air density and wind velocity measurements. As a consequence, Eq.(1) becomes valid. In the general random formulation of Eq.(7), r, plays the most important role depending on its actual value between –1 and +1. Evidently, both air density and wind speed are inversely proportional. Since, moist air is lighter than dry air, the moisture plays a great role in the air, giving rise to higher wind velocities. Hence, the cross correlation is expected to have negative sign between wind speed and air density. As a result, Eq.(2) will give greater values than Eq. (7) which can be rewritten as: ⎡ S S ⎤ 1 ρ 3 E P = E(ρ)E(V 3)⎢1 + r V ⎥ (9) () ⎢ ⎥ 2 E(ρ ) E(V 3) ⎣⎢ ⎦⎥ The term within the brackets can be defined as the correction factor α namely: S S ρ 3 α = 1 + r V (10) E ( ρ ) E (V 3 )

The coefficient of variation, C, is defined as the ratio of the standard deviation to the arithmetic average. Two of such ratios appear in Eq. (10) as the coefficient of variation of air density Cρ and of wind speed cubeC . Hence one can write Eq. (10) as: V 3 α =1+ rC C (11) ρ V 3 Eq.(11) indicates that in the case of small variation of the coefficient in particular smaller than one, the second term on the right hand side becomes negligible. On the other hand, for relatively big coefficients of variation, the second term may amount to a significant level, which means that the traditional formulation overestimates the wind energy potential. Evidently when r = 0 the relative error becomes zero. This work provides a basis for estimating the size of correction factor for a given pair of air density and wind speed time series records.

Now in order to evaluate E(ρ), we can use the concept of expectation value in the universal gas law [23] on the form : E ( p ) E ( ρ ) = (12) R .E (T ) Where p is the air pressure measured in Pascal unit ,T is the air temperature measured in Kelvin and R=287.04 J.K-1.(Kg)-1. is the universal gas constant.

MATHEMATICAL AND STATISTICAL ANALYSIS OF WIND DATA

The Weibull probability function [25] is one of two most commonly used in wind speed analysis, it is on the form: k −1 k ⎛ k ⎞⎛ v ⎞ ⎡ ⎛ v ⎞ ⎤ f ()v = ⎜ ⎟⎜ ⎟ exp⎢− ⎜ ⎟ ⎥ (13) c c c ⎝ ⎠⎝ ⎠ ⎣⎢ ⎝ ⎠ ⎦⎥ Where v is the wind speed (m/s), k the shape parameter (dimensionless) and c the scale parameter (m/s).

The mean and variance of wind speed are:

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

x ∫ f ()v vdv v = 0 = cΓ 1 + 1 (14) m Lim x () x→∞ k ∫ f ()v 0

2 2 2 σ = c ⎡Γ()1 + 2 − Γ (1 + 1 )⎤ (15) ⎣⎢ k k ⎦⎥ Where Γ - is the gamma function. The values of k and c can be evaluated using the following formulae [90,100]: k = σ / v −1.086 (16) ( m )

c = vm / Γ(1+1/ k) (17) 3 The mean value of v becomes: v3 = c3Γ()1+ 3/ k (18)

Consequently, the mean wind energy potential of airflow through a unit of surface area perpendicular to the air stream during unit time is given as [24]:

P = ρv3 / 2 (19)

Where ρ is the air density (kg/m3).

The cumulative distribution Weibull function is:

v F()v = ∫ f ()v .dv 0 F()v = 1− exp[− (v / c)k ] (20)

The annual cumulative distribution Weibull function is:

T()v = 8760h / y [1− exp(− (v / c)k )] (21)

For many sites it is adequate to reduce equation (13) to the one parameter Rayleigh distribution by setting k=2, [25]. Hence equations (13), (17) and (18) become:

2 2v ⎡ ⎛ v ⎞ ⎤ f v = exp − (22) () 2 ⎢ ⎜ ⎟ ⎥ c ⎣⎢ ⎝ c ⎠ ⎦⎥

c =1.13vm (23)

3 1/ 3 (v ) =1.24vm

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

DEGREE OF DEPENDENCY

Variable Precision Rough sets (VPRS):

A generalized model of rough sets called variable precision model (VP-model) [27], aimed at modeling classification problems involving uncertain or imprecise information. The generalized model inherits all basic mathematical properties of the original mode introduced by Pawlak. The basic concept introduced in (VPRS) is rough inclusion. Its definition lies on criterion C(X,Y) called relative classification error, defined as follows: C(X,Y) = 1-card(X∩Y)/card(X) if card(X) > 0 C(X,Y) = 0 if card(X) = 0 Being X and y two subsets of the reference Universe U. According to this concept, the traditional inclusion relation between X and Y is defined as: X ⊆ Y if and only if C(X,Y) = 0

Rough inclusion arises naturally by loosening the traditional inclusion in when an admissible error level is permitted in classification. This error explicitly expressed as β. Then, the rough inclusion relation between X and Y, s defined as:

X ⊆ β Y if and only if c(X,Y) ≤ β Ziarko established as a requisite that at least the 50% of the elements have to common elements, then being 0 ≤ β < 0.5. Under this assumption, we are going to generalize the definition of lower and upper approximation, receiving the names of β-upper approximation, respectively. Let be a knowledge base k = (U,R) and a set X ⊆ U, the β-lower approximation of X, (denoted by

Rβ X R β X ) and the β-upper approximation (denoted by ) are defined as follows: R X = ∪{Y ∈ IND(R) : Y ⊆ X} β β R X = ∪{Y ∈ IND(R) :c(X ,Y) < 1− β} β Alike in the pawlak’s model, the reference universe U could be divided in three different regions regarding its lower and upper-approximations. These are positive region POSR, β(X), the negative region NEGR, β(X) and the boundary region BNDR, β(X), defined as follows:

Rβ X POSR, β(X) =

NEGR, β(X) = U − Rβ X

BNDR, β(X) = Rβ X − Rβ X These new definitions yield to a reduction of the boundary region allowing more objects to be classified as X members. A drawback it the classification obtained is not entirely exact, since a classification error is introduced (but never great than β ). The degree of dependency of p on q is given by:

card pos (q ) γ ()p ,q = β , p (24) β card U where:

Using equation (24) to estimate the dependency of the wind Energy P on the both cube wind speed u3 and the air density ρ.

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

Cairo Kosseir Hurguada

Posp (u3) C=356 β=0.15 C=331 β =0.1 C=329 β =0.17 γ 0.973 0.907 0.901

RESULTS AND DISCUSSION

The random variability in the actual daily temperature, pressure, air density and wind speed measurement time series as recorded at meteorological station, Cairo Airport , Kosseir and Hurguada, Egypt, at longitude 31o 24\ , 34o 18\ and latitude 30o 17\ , 26o 08\ respectively are presented for complete year of 2005 in Figs. (2-5). It is to be noted that Cairo, Kosseir and Hurguada, stations have an average velocity 3.633 m/s, 4.47 m/s, and 6.171 m/s respectively. Temperature, pressure and air density time series exhibit within year seasonal variations rather distinctively; the wind speed fluctuations are quite stationary without explicitly observable periodicities or trends. This feature of the wind speed supports the use of Eq. (2) as a rough approximation for wind energy calculation.

Table 1, presents the statistical properties of air density, wind velocity cube and the potential energy. Consequently, the cross-correlation, r, between the air density and cube of the wind velocity time series is equal to –0.01861, 0.079556, and -0.1052 for Cairo Airport, Kosseir and Hurguada respectively.

The variations of the wind speed are comparatively very much larger than the air density variations. As a first impression, since the variations in the air density are very small, one might ignore these variations and assume a constant air density equal to the arithmetic mean which is 1.1973 kg/m3, 1.1866 kg/m3, and 1.187 kg/m3 for Cairo, Kosseir and Hurguada, respectively. As shown in Table 1, however, although the variations in the air density are small their impact on the wind energy calculations might be significant. In order to confirm this point, let us apply first Eq. (11) to the data given in Table1.

The coefficient of variation of air density and velocity cube series for Cairo Airport , Kosseir and Hurguada stations are Cρ=0.028/1.197= 0.0232, Cρ=0.025/1.187= 0.0211,

Cρ=0.025072/1.186592=0.02113 and C = 25.539/36.996= 0.6844, C =25.539/36.996= 0.6844, v3 v3 C = 311.4663/332.0811= 0.937922, respectively. v3 Hence, the substitution of these values and cross-correlation value into Eq. (11) yields a correction factor α. Hence Eq. (9) gives, P (E) =36.938 W/m2 =132.98 kWh/m2, P (E) = 71.852W/m2 =258.667 kWh/m2, P (E) = 195.572 W/m2 = 704.061kWh/m2 for Cairo Airport, Kosseir and Hurguada respectively.

These data are presented hourly for the complete year of 2005. The height of anemometer was 10 meters above the ground. The data were used to evaluate the frequencies of wind speeds as well as the monthly (Fig 2) and annual mean wind speed and power. Evidently, the minimum value of the average monthly wind speed is 2.483 m/s, 3.976 m/s for Cairo and Hurguada respectively for December and the maximum average value is 4.6 m/s, 5.089 m/s for Cairo and Hurguada respectively for Mars.

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

Fig.(1) Location of Cairo Airport, Kosseir and Hurguada meteorological station.

Table 1. Statistical data of air density, wind velocity cube and potential energy at Cairo Airport, Kosseir and Hurguada-Egypt

(a)Cairo (b) Kosseir

Air Velocity Potential Air density Velocity Potential Parameter density Parameter cube(m/s)3 Energy (kg/m3) cube(m/s)3 Energy (kg/m3) Average 1.197 61.701 36.996 Average 1.187 120.535 71.603 Median 1.195 50.141 29.953 Median 1.186 76.766 44.735

Mode 1.181 81.102 48.298 Mode 1.204 64.000 12.646

S.D. 0.028 42.225 25.539 S.D. 0.025 140.163 84.029

Maximum 1.257 321.725 198.735 Maximum 1.238 1076.891 654.508

Minimum 1.144 12.326 7.397 Minimum 1.146 5.359 3.183

(c)Hurguada

Parameter Air density (kg/m3) Velocity cube(m/s)3 Potential Energy Average 1.187 332.081 195.572 Median 1.186 244.141 143.500 Mode 1.204 561.516 6.850 S.D. 0.025 311.466 182.883 Maximum 1.238 1622.234 980.543 Minimum 1.145 1.953 1.152

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

Table 2 Potential Energy (kwh/m2), cross correlation (r) and alpha (α) factors for Cairo Airport Kosseir and Hurguada

parameter Potential Energy (kwh/m2) cross correlation (r) Correction factor (α) Cairo Airport 133.180 -0.01861 0.998456 Kosseir 257.769 0.079556 1.00348 Hurguada 704.061 -0.1052 0.995577

40.00 40

35.00 35

30.00 30 C) o

25.00 C)

o 25

20.00 20

15.00 15 Temperature ( ( Temperature

Temperature 10.00 ( 10

5.00 5

0.00 0 1 51 101 151 201 251 301 351 1 51 101 151 201 251 301 351 Julian day Julian day Fig. 2 (a) Daily temperature time series (Cairo) (b) Daily temperature time series (Hurguada)

1025 1030.00

1025.00 1020

1020.00 1015

1015.00

1010

1010.00 (mb)Pressure Pressure (mb) Pressure

1005 1005.00

1000.00 1000 1 51 101 151 201 251 301 351 1 51 101 151 201 251 301 351 Julian day Julian day Fig. 3 (a) Daily pressure time series (Cairo) (a) Daily pressure time series (Hurguada)

1.25 1.25 ) ) 3 3

1.20 1.2 density (kg/m density (kg/m density

1.15 1.15

1.10 1.1 1 51 101 151 201 251 301 351 1 51 101 151 201 251 301 351 Julian day Julian day Fig. 4 (a) Daily density time series (Cairo) (b) Daily density time series (Hurguada)

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

8.00 14

7.00 12 ) 6.00 10 m/s

5.00(

8 4.00 eed p 3.00 6 wind speed (m/s) speed wind 2.00 4 wind s wind

1.00 2

0.00 1 51 101 151 201 251 301 351 0 julian day 1 51 101 151 201 251 301 351 julian day Fig. 5 (a) Daily wind speed time series (Cairo) (b) Daily wind speed time series (Hurguada)

300 hurgada

250 Qosseir Cairo

200

150

Potential Energ Potential 100

50

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec month Fig. (6) Variation of the potential energy with months

Fig. (6) Shows that the variation of potential energy on Cairo, Kosseir and Hurguada stations. It's found that t he value of the potential energy in Hurguada is greater than Cairo and kosseir through the year, and also kosseir is greater than Cairo through the year accept in December. Cairo Hurguada 5.00 8.00

4.50 7.00

4.00 6.00 3.50

5.00 eed m/s

eed m3.00 /s p p

2.50 4.00 e wind s wind e

e wind s wind e 2.00

g 3.00 g

1.50 2.00 Avera Avera 1.00

1.00 0.50

0.00 0.00 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Month Fig. (7) The average monthly wind speed

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

The daily wind speed at Cairo Airport in April, and Hurguada in June are shown in 4.600 m/s, 7.150 m/s respectively, and the annul average are 3.633 m/s, 6.171 m/s respectively. Fig. (9) is the annual frequency distribution of wind speed showing that more than 98%, 98.5% respectively, of the annual wind speed is in the range of 1.0 to 7.0 m/s, 1.5 to 11.75 m/s respectively.

Cairo Hurguada 8.00 13.00

7.00 11.00

6.00 9.00

5.00 7.00

4.00 5.00 Daily wind speed, m/s speed, wind Daily Daily wind speed, m/s speed, wind Daily

3.00 3.00

2.00 1.00

5 5 05 5 05 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 0 0 00 00 00 00 00 00 00 00 /200 /200 2 2 2 00 3 5/2 7 9/2 /2 /2 /2 9/200 5/2 /2 /200 200 200 4/1/200 4/ 4/ 4/ 4/ 11 13 17 1 21/ 23/ 2 29 3/200 5/200 7/200 9/2 4/ 4/ 4/15/200 4/ 4/ 4/ 4/ 4/ 4/27/ 4/ 6/1/200 6/ 6/ 6/ 6/ 11/200 13 15/200 19/200 21/ 23/200 25/200 27/200 29/ Day 6/ 6/ 6/ Day6/17/200 6/ 6/ 6/ 6/ 6/ 6/ Fig. 8 Daily variation of the wind speed in Cairo Airport, Kosseir and Hurguada at December 2005. Cairo Hurguada 25 20

18

20 16

14

15 12

10 Frequency, % Frequency, 10 % Frequency, 8

6

5 4

2

0 0 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 1.25 2.25 3.25 4.25 5.25 6.25 7.25 8.25 9.25 10.25 Wind speed, m/s Wind speed, m/s Fig. 9 Annual distribution of wind speed.

Comparison of Weibull, Rayleigh, and the actual data distribution are shown in Fig. (10). It is clear from the figure that the Weibull distribution is the best match with the actual data.

Fig. (11) Describes the average monthly wind power. The maximum wind power is 67.695 W/m2 in December, 274.5216 W/m2 in June for Cairo Airport, and Hurguada respectively. While the minimum wind power is 16.542 W/m2 in February, 79.428 W/m2 in January. The mean annual wind power is 36.996 W/m2, 195.572 W/m2 respectively. Table (1) describes the mean values of wind speed and the corresponding average annual wind power for each distribution. It can be concluded that the Weibull distribution was suitable for representing the actual probability of wind speed data at Cairo Airport, Kosseir and Hurguada in 2005.

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

Cairo Hurguada 0.4 0.4

3 2 Weibull = 0.006x - 0.0971x + 0.4408x - 0.4329 2 0.35 Weibull or rayleigh = -0.0069x + 0.1026x - 0.2146 0.35 R2 = 0.3535 R2 = 0.2918 Actual data Actual data 3 2 0.3 0.3 Rayleigh = -0.0039x + 0.023x + 0.0338x - 0.0931 R2 = 0.4472

0.25 0.25 function function y

y 0.2 0.2 Weibull distribution Weibull Rayleigh Rayleigh distribution distribution 0.15 0.15 distribution Probabilit Pro bab ilit 0.1 0.1

0.05 0.05

0 0 1234567135791113 Hourly wind speed m/s Hourly wind speed m/s Fig. 10 Wind speed frequencies.

Cairo Hurguada

120 450 Actual data Actual data Weibull 400 Weibull Raleigh 100 Raleigh 350 ) ) 2 80 2 300

250

60

200

Wind energy potential (w/m potential Wind energy 150

Wind energy (w/m potential 40

100

20 50

0 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Month Fig. 11 Average monthly wind energy potential.

Table 3. Average wind speed and corresponding power.

Average wind velocity m/s Average wind power W/m2 Cairo 3.633 36.996 Actual data Kosseir 4.465 71.603 Hurguada 6.171 195.572 Cairo 3.937517 38.61823 Weibull Kosseir 4.901237 72.08195 distribution Hurguada 7.57166 275.9581 Cairo 4.506157 57.88203 Rayleigh Kosseir 5.536236 103.8851 distribution Hurguada 7.648649 278.956

VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

CONCLUSION

The random wind energy potential formulation has been presented in a general form and its reduction to the classical approximations is shown in detail. It has been observed that in the conventional wind energy potential calculations, the air density is mostly assumed constant which simplifies the wind energy formulae derivation and forces the energy to depend on the wind speed cube only. In this work, the average wind energy production is not only a function of the coefficient of variation of the air density and wind speed cube but also on the cross-correlation coefficient. In case of independency of both air density and wind speed variations, wind energy is obtained simply employing average air density measurements instead of standard constant air density.

Results of the wind energy obtained at this work encourage building up a power wind station at Hurguada, Egypt.

The wind speed at Cairo Airport, Kosseir and Hurguada -Egypt has been studied for 2005. Statistical analysis was carried out to determine the monthly, annual and probability of wind characteristics. The annual average wind speed was of 3.633 m/s, 4.465 m/s, 6.171 m/s respectively. Finally, The Weibull distribution is suitable for representing the actual probability of wind speed data.

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VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt

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