Energy Convers. Mgmt Vol. 33, No. 1, pp. 1-5, 1992 Printed in Great Britain. All rights reserved DAILY AND HOURLY 0196-8904/92 $5.00÷ 0.00 Copyright ~ 1992 Pergamon Press plc WIND SPEED DISTRIBUTION IN BAHRAIN Y O U S E F A. G. A B D A L L A I and B. S. ATTILI 2 I Mechanical Engineering Department, University of Bahrain, P.O. Box 32038, Isa Town, Bahrain and 2Mathematics Department, King Fahd University ofPetroleum and Minerals, Saudi Arabia (Received 26 July 1990; received for publication 26 February 1991) A~traet--The characteristics of daily (for I 1 yr) and hourly (for 8 yr) wind speed data, recorded at the Meteorological Office of the Civil Aviation Directorate, Bahrain, have been studied. It shows a very high daily fluctuation of wind speed for the winter months. The daily wind speed starts and ends high for most days of the month. It drops in the first and last 10 days of the month, and then remains almost constant in the mid-10 days of the month. The hourly wind speed attains its maximum value at around 10-12 h local time. A mathematical model is obtained for prediction of wind speed at any hour of the day. The following equation can predict the wind speed at any hour of the day using local time: u = 0.001349 t 3 - 0.06227 t2+ 0.7568 t + 3.253. INTRODUCTION A large potential of power is contained in the movement of air in the form of wind. In the beginning, wind was used to drive sailing boats, pump water, and grind grains. The Persians built the first known windmills as early as 250 B.C. [1] for those purposes. Later, it was used to generate electricity. The first generation of electricity from a windmill occurred in 1890 in Denmark [2], which led to the spread of windmills for various uses. Using wind energy has many advantages, such as not depleting natural resources and not causing environmental pollution. Wind is one of the main renewable energies available in Bahrain, but it is not yet considered seriously because of cheap fossil fuels. Since the fossil fuel is coming to an end in the near future, alternative sources of energy should be studied. Publications by Abdalla [3] and Abdalla and Attili [4] deal with the characteristics and evaluation of wind energy in Bahrain. It was concluded that Bahrain has frequent strong winds during the summer months especially in June and July (locally known as Shamal, which means wind coming from the north). The winter months of November-January show a strong wind with wide variations in both speed and direction. Wind machines cannot be designed on the basis of mean wind speed alone. Detailed statistical information must be carefully weighed against any design based on mean wind speeds. This type of information must also be heavily considered for daily and even hourly changes in speed, although this is more difficult to analyze. All the previous analyses for Bahrain were done only for yearly and monthly variations of wind speed. The present work analyzes data for daily and hourly wind speed to contribute to the existing information on the available wind energy data as presented by Refs [3, 4]. DATA COLLECTION The data used in this paper is collected from the Meteorological Office of the Civil Aviation Directorate of the State of Bahrain. The hourly wind speed data used in this study are for 8 yr (1976-1983), whereas the daily wind records are for 11 yr (1976-1986). The cup anemometer was used to measure the wind speed at a height of 10 m. ECM 33/I--A 1 ABDALLA and ATTILI: W I N D SPEED D I S T R I B U T I O N IN B A H R A I N (a) {b) 14 14 12 \/~e e.. 12 ~% 10 10 8 July ~ /•% , i ' " " / ' . - ~ ,*"•,,. \/ 8 doruJary 6 ,.,......*.•,* ",.,.-e 6 /~ 14 12 ~,. . . . , . 10 February / ~,\ k/~',,/ . .. ;-~, ". ~ V 10 , August -':, .,.....,." B . e~e-/e~e'ce" Morch • . "~e"e.°.,.k:,.v!'.,:,: 10 8 ~ a .,-.., 10 F1k I 1"~V :'.v '°1""\7* ",,/".,<,.,.d \d *"°'d .... * ...,, , ~ ~.o .,*--.-..o-o.4 k V""°"-...I • \ 10 .. io- "•',.3 8 J I I I I 6 12 18 24 30 /e\ November e"° se, ~,,.,.,.,-.'\ : ..,2. -.... : \ ..., / :/\,1 December 12 e _3..."\it'. " --o-o" 6 May '*'/ 0.0.* October 8 8 L- "-.-,.,., I \.,......1 / 4 6 T"% \,,,.,..,, ..."."\ ./",,, ;~ 6 •%/ 6 ., ",.O.o / o.,. 4 \./ :~.,..;,,.,w.~.v \ L ...- 4 o o° "e,o o .... .,o *% ,.o April ~o ,.,. September 10 12 .,./,., ,.:~.--.,. 6 ".-d 8 ! _o/ek J.oe O. • 0"* "x \ O~S /o 0"* \ :v / 8 I 6 I 12 6 Days of the month • e~ •/ • I \r"'Y I I 24 18 I 30 Days of the month Fig. 1. Daily mean wind speed of (a) January-June; (b) July-December. RESULTS AND DISCUSSION Daily data analysis The daily m e a n wind speed data is important, since the variation o f hourly speeds can be described from it. Furthermore, the daily means and standard deviations are indicators o f the wind 11 100 ! Io ; ~- 90, ,.,.i,.,.,.: .,.., .,,,.,./ ,.,i,: E -~ 80 70 | /",./ • -o ~o \! v I 5 I 9 I 13 I 17 I 21 D O ~ of the m~nth Fig. 2. Daily mean wind speed. I 25 II 29 31 .50 / ", • o-o V I i I I I I 5 9 13 17 24 25 Deys of the month Fig. 3. Daily mean power density. I I 29 31 ABDALLAand ATTILI:WIND SPEED DISTRIBUTION IN BAHRAIN 3 power supply potential over a 24 h period. Figures 1(a) and (b) show the daily mean wind speeds for different months of the year. They indicate a similarity in variation of blowing wind in January and February, March and April, and August-October, where the fluctuation is less than for the other months. The fluctuation is very high in the winter months. Daily mean wind speed is plotted and shown in Fig. 2. It shows that the wind speed starts and ends high for most of the days of the month. It drops in the first and last 10 days of the month, and then remains practically constant in the mid-10 days of the month. Figure 3 shows the daily variation of mean power density. Hourly data analysis Hourly wind speeds for 8 yr (1976-1983) were plotted against the hour of the day (local time) and presented in Fig. 4. It shows that the speed has a regular diurnal variation, and it attains a maximum value around 10-12 h local time (GMT + 3h). In all cases, there appears to be a seasonal effect. From September to November, the wind is relatively weak, but it becomes stronger from December to March. The strongest wind appears to be in June and July because of Shamal winds. In the summer months there is a clear difference in wind speed between day and night times because of the high solar intensity during the day time. Figure 5 shows the mean hourly wind speed for all days during 8 yr (1976-1983). The mean wind speed dips to its minimum at around 20-21 h local time, and then it picks up slowly during midnight and early morning until it reaches its maximum at around 10-11 h local time. Peak hourly winds take place during the day time because of the solar radiation effect in terms of an increase in the diurnal wind speed profile. Such patterns of diurnal wind speed are expected, especially for summer days with high solar radiation intensity. Hourly mean power density is plotted and shown in Fig. 6. It illustrates that small changes in wind speed results in much bigger variations of wind power, because the power is proportional to the cube of the speed. Mathematical model Prediction of wind speed at any hour of the day is possible if the curve in Fig. 5 is fitted correctly by any of the curve fitting techniques. Since we know that such data does not plot linearly, then fitting by a curve is more reasonable. Fitting by polynomials has been chosen, since they can be readily manipulated. For given set of points (ti, Ui), where t~is the local time in hours of the day and U~is wind speed at that time, the least-squares technique for fitting nonlinear curves are used. In this development, n is used as the degree of the polynomial and N as the number of data points. It can be noted that N > n + 1, because if N = n + 1, it will be more proper to used interpolation of polynomials. Assuming the functional relationship as: u = ao + a l t (1) + a2 t2 + . • • + a , t n with errors defined by: ei = Ui - ui = Ui - ao - al t2i - a2t~ . . . . . (2) a,t'/ where u~ is the observed or experimental value of wind speed corresponding to ti, where ti is free of error. The method of least-squares simply minimizes the sum of squares of the errors e~, that is, min S(a0, a,, 02. . . . . a , ) = Z e~= ~ ( U ~ - a o - a ~ t g - a 2 t ~ i=l ..... a,t'/) 2 (3) i=1 over the constants a0, a~. . . . . a,. At the minimum, all the partial derivatives OS/~ao, dS/3a~ . . . . . OS/Oa, vanish. Writing the equations for these gives (n + 1) equations. Simplifying these equations in matrix form, it will give: Z,t i Ly~t'/ t llaoI Z,t~ "i~t~ "'" Zt'/+' a, Z,l'/+' z,t'/+2 ... Z,t~" an = I Z't,U, I" Lz,t'/ui_] 4 A B D A L L A and ATTILI: W I N D SPEED D I S T R I B U T I O N IN B A H R A I N .\ ~ / [/" /0/o / J o / / ./" t p , / I le t 3I *~. \ °\ -r t\ \. ° J\ ",., •~. "\ I \ ~ o m ~ I ~ I o o I m I I I I I 0 ~ ~O I I O QD ~ I I e~ 0 "-" ~ ~ ($~.ou)l) peeds puIM g ¶ / ? I / / /,/o /. i / F \ l P / ") / ,/ /o t _ ~ /o ® 1 \ -~ i. \ \ \ "~. \ ,~ "\ ¶ I o~ Ox - I ! o I I I I I ~ 0 I I I I I ~ (s~ou~} peeds PuIM I I I I N I I I "~ ,~ ~ ABDALLA and ATTILI: WIND SPEED DISTRIBUTION IN BAHRAIN 5 13 • 12 o=.. • •%• / \ / 11 / 10 \ / \ / 9 8 o o \ 200 - - 150 oso-°" Q"bO % ',. ° o/ ,oo / o,.O/ ~o \ ",, .o~O S• %°%o • • • • • °° - . . ~ - I I [ I t I I 4 8 12 16 20 24 0 I I I 1 I I I I 2 4 6 8 10 12 Hours of the doy I I 14 16 I I 18 20 I I 22 24' h Fig. 5. Mean hourly wind speed. Fig. 6. Hourly mean power density. The problem will now be solving a set of linear equations for a0, a~ . . . . , a, which will be used in the functional relationship, equation (1). In this case, the Gaussian-elimination with scaled column pivoting is used to solve the problem. To decide which degree polynomial is the best, the principles of statistics are used; that is, the degree of the approximating polynomials is increased until a significant decrease in the variance, a 2, is noticed. The variance is computed in this technique as: o.2= ~ e2 N - n - 1" (4) The values of n tried in this case are n = 1, 2 . . . . ,6, and it turned out that o.2 is the least when n = 3 for 8 yr data. The equation obtained from the technique is: u = 0.001349 t 3 -- 0.06227 t 2 + 0.7568 t + 3.253. (5) Using this equation, the wind speed can be predicted at any hour of the day using local time. CONCLUSION The wind speed in Bahrain is fairly good to be used for small or relatively medium size applications of wind energy conversion systems. The daily analysis of wind speed shows a high fluctuation in the winter months. It drops in the first and last 10 days of the month, whereas it remains almost constant in the mid-10 days of the month. The hourly wind speeds show a regular diurnal variation, and it attains a maximum value at around 10-12 h local time. A polynomial equation of third order is obtained to predict wind speed at any hour of the day using local time. REFERENCES 1. 2. 3. 4. R. C. Dorf, Energy, Resources d Policy. Addison-Wesley, Reading, Mass. (1978). J. C. McVeigh, Sun Power: An Introduction to the Application of Solar Energy. Pergamon Press, London (1979). Y. A. G. Abdalla, Proc. Second Arab Int. Sol. Energy Conf., Bahrain (15-21 February 1986). Y. A. G. Abdalla and B. S. Attili, Second A S M E - J S M E JSES Sol. Energy Conf., U.S.A. (22-27 March 1987).