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

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Assessment of Wind Speed and Wind Power Through Three Stations in Egypt, Including Air Density Variation and Analysis Results with Rough Set Theory VIII Radiation Physics & Protection Conference, 13-15 November 2006 , Beni Sueif-Fayoum, Egypt 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 Egyptians used wind energy in windmills for grinding grain and pumping water from the river Nile 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 Middle East 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 renewable energy 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.
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