International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 12, Issue 1, January 2021, pp. 870-887, Article ID: IJARET_12_01_079 Available online at http://iaeme.com/Home/issue/IJARET?Volume=12&Issue=1 Journal Impact Factor (2020): 10.9475 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6480 and ISSN Online: 0976-6499 DOI: 10.34218/IJARET.12.1.2021.079
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ANALYSIS OF WIND POWER AND WIND POWER CHARACTERISTICS: AL-AQIQ CITY, SAUDI ARABIA
Saeed A. Al-Ghamdi Department of Electrical Engineering, Faculty of Engineering, Albaha University, Albaha, Saudi Arabia
ABSTRACT The annual monthly and yearly mean wind speed variations in King Saud airport, Al-Aqiq, KSA are collected and studied to investigate the feasibility to generate electrical power. Average wind speeds and wind power have been determined daily, monthly and annual. The parameters of the shape and scale of the Weibull density distribution function and the scale of the Rayleigh distribution function have been calculated. Comparison of the Weibull model with Rayleigh's distribution of wind power densities. The comparison revealed that the Weibull distribution function well reflects wind data as compared to Rayleigh density distribution. The mean wind speed for the Al-Aqiq region is about 3.39 m/s over a 38-year time period with a main direction of southwest. The diurnal study showed that the wind speed remains above 3.0 m/s from 09:00 AM to 10:00 PM and below it during the rest of the day's hours. A seasonal analysis shows that in summer, the wind speed is highest (4.41 m/s with a mainly north- northwest direction). The generation of wind energy by Aeronautica Windpower, Dewind, Enercon, Soyut Wind, Nordex and SouthWest at a hub height of 50 m has been considered for 15 wind machines of various sizes. The highest capacity factors (35.31%) were calculated for Soyut Wind 250 (773.370 MWh/Year). These results indicate that it is feasible to generate power from wind energy in the Al-Aqiq region for providing energy demands. Key words: Statistical analysis, wind mapping, wind power, windrose, Weibull, Rayleigh. Cite this Article: Saeed A. Al-Ghamdi, Analysis of Wind Power and Wind Power Characteristics: Al-Aqiq City, Saudi Arabia, International Journal of Advanced Research in Engineering and Technology, 12(1), 2021, pp. 870-887. http://iaeme.com/Home/issue/IJARET?Volume=12&Issue=1
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1. INTRODUCTION Recognizing the value of renewable energy, especially wind, the authorities in Saudi Arabia will invest billions in this promising energy sector. The output of electricity from wind would save oil which can be exported to raise national income. Moreover, the generation of electricity from wind energy would decrease the pollution of the environment which could be produced from conventional power plants. Weather conditions and wind power were studied and modelled using a linear regression technique to model the weather parameters [1]. The assessment of wind power on Saudi Arabia's east coast indicated that the average wind power attainable might be 70.6 W/m2 [2]. The availability of wind power in the area of the east coast of Saudi Arabia is 55% while solar power availability is 39%. The Saudi Arabia wind map shows that the Kingdom is distinguished by the presence of two vast windy regions along the coastal areas of the Arabian Gulf and the Red Sea [3,4]. In these two windy areas, the average annual wind speed exceeds 4.65 m/s and varies from about 3.9 to 6.13 m/s over these areas. Jubail Industrial City's wind characteristics and resource evaluation were represented utilizing calculated hourly average wind speed data [5,6]. With the wind prevailing in the north-west direction, the availability of wind speeds above 3.5 m/s was more than 75 %. From a 3 MW wind machine at this location, the energy production was found to be 11,136 MWh/yr. With a 41.3 % capacity factor for the plant. In addition, hourly mean wind-speed data recorded at the Dhahran, Saudi Arabia meteorological monitoring station were analyzed to document monthly variations in wind speed and solar radiation, likelihood of wind speed distribution, and to examine the feasibility of using wind-solar energy conversion systems [7,8]. To conduct all the calculations and optimization needed to accurately design the wind energy system and match sites and wind turbines, a computer program has been implemented [9-11]. This software is designed in a generic form that enables it to be used in the entire world with an infinite number of sites and wind turbines. The criteria for selecting the most appropriate wind turbine for each site are that the maximum capacity factor and the minimum energy costs are given by the wind turbine and the site. In terms of annual, seasonal and daily changes in Yanbo, a long-term wind data study was presented [12], international airports in the Kingdom [13,14], Dhahran, Yanbo, Al-Wajh, Jeddah, and Gizan [15], Rafha [16], Dhulom, Arar, Juaymah, Rawdat Ben-Habbas, and Dhahran [17], Saudi Arabia. The analysis of energy output demonstrated high production of wind turbines of smaller sizes than larger wind farm. Likewise, compared with larger ones, higher capacity factors have been acquired for smaller wind machines. Wind power in Saudi Arabia could be produced at most sites with 25-50.3 % of the plant capacity factor [13,14]. In the north-eastern area of Saudi Arabia, vertical axis wind turbines of small rated power have been utilized to classify suitable and effective ones for power generation [18]. In order to recommend an acceptable hub height, the impact of hub height on energy production and the plant capacity factor has been examined. For almost 10 sites in the Saudi Arabia, the statistical properties have been computed and observed to be consistent with the actual diurnal variance in average wind speed. For almost all sites, the predicted wind values derived from these autoregressive models have been compared with the observed wind data and have been shown to go into very good agreement [19]. In addition, a statistical analysis of wind speeds was carried out, including the adaptation of the cumulative distribution function observed to the Weibull distribution function using the least square technique, the determination of Weibull variables and the assessment of wind power density using two approaches [20]. Yanbu has the largest resource on the east coast, whereas Makkah has the lowest wind energy density impacted by the Sarawat Mountains. In order to study wind properties and wind energy production, a measured value of wind speed at different heights above ground level was used along with other meteorological variables [21].
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Real representatives of the actual distribution of wind frequency have been found to be Weibull parameters. The Weibull density distribution function's shape and scale parameters are determined for ten sites in Saudi Arabia [22]. It is inferred from this research that the Weibull distribution function reflects wind data very well. The wind energy potential of Saudi Arabia's Eastern Province has been investigated. A suitable distribution of Weibull and Rayleigh is produced on the basis of data obtained at a coastal location in northeastern Saudi Arabia for a complete year. The error in utilizing the Rayleigh approximation is found to be less than 10% of the total rated power density level [23,24]. In previous work for the author, the analysis of data recently obtained at three locations in Albaha region, Saudi Arabia was presented [25,26]. Results showed that the highest average wind speed has been recorded at Almorassaa site at a value of 3.88 m/s in direction between NW and WNW. The highest average monthly wind speed is recorded at Albaha University, Al- Aqiq in March, with values of 5.11 m/s at a height of 10 m, the main wind direction is southwest. The highest capacity factor is recorded as 26.0% for Aeronautica Windpower 33-225 wind machine. The aim of this study is to evaluate the potential of wind energy in the Al-Aqiq area, KSA, in terms of annual, seasonal and diurnal changes, and to analyze wind availability and then use the findings to calculate the distribution of wind energy in the Al-Aqiq region using the measured distributions of Weibull and Rayleigh.
2. SITE DESCRIPTION AND METEOROLOGICAL MEASUREMENTS Al-Aqiq is a significant town in the Kingdom of Saudi Arabia's south-western area, located at King Saud Airport, Fig. 1. The King Saud airport's latitude and longitude are 20° 17´ 41˝ North and 41° 38´ 35˝ East and 1651.88 m above sea level. Meteorological activity data reported in the period 1983 to 2019 were collected for the purposes of this study. The parameters were measured at 10 m above the surface of the ground including wind speed, wind direction, relative humidity, temperature, pressure, rain and many others. Wind speed and direction records have been used for a total of 444 months. The data was obtained from the King Saud airport from year 1983 to 2014) and NASA Prediction of Worldwide Energy Resources from year 2015 to 2019 (https://power.larc.nasa.gov/).
Figure 1 Geographical locations of meteorological stations.
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In summer, the Al-Aqiq climate is rather hot and in winter rather cold. The registered temperatures ranged from a minimum of 13.50°C (1992) to a maximum of 31.30°C in 2017, with an average of 23.0°C in the general weather conditions. The highest temperature in June, July and August and the lowest in January were registered; see Fig. 2(a). The surface pressure changed from 848.37 mBar in year 2013 to 860.41 mBar in year 2010 with a mean value of 853.30 mBar. The lowest pressure values were recorded in July, and the highest pressure was in December, see Fig. 2(a). The relative humidity varied between 0.00% and 75.0% in year 2013, with a nean value of 35.09%. The lowest humidity percentage in December and the highest value in January were recorded; see Fig. 2(c). Figure 3 show the mean yearly temperature, pressure and humidity from 1983 to 2019. It is obvious that the temperature and humidity tend to slightly increase while pressure decreases from year 1983 to 2019.
35 35
) 1983-2019 ) C C
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y y t t i 60 i 60 d d i i m m u u 40
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e e g g a a 20 r 20 r e e Av 1983-2019 Av 0 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Year (c) Relative humidity. (c) Relative humidity. Figure 2 Average monthly wind speed, Figure 3 Average yearly wind speed, temperature, station pressure, and relative temperature, station pressure, and relative humidity during a year (average from 1983 to humidity (from 1983 to 2019). 2019).
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3. METHODOLOGY AND MATHEMATICAL MODELS 3.1. Calculation of Wind Power Using measured data, the monthly average wind speed values and standard deviations were determined from Eqs. (1) and (2), Table 1. The Weibull distribution function is represented mathematically as seen in Eq. (3), a two parameter function. By integrating Eq. (3), the cumulative distribution function is obtained and takes the form as in Eq. (4). In terms of the gamma function, the average of the Weibull distribution, i.e., the average wind speed has been represented and has been given by Eq. (5). The distribution of Rayleigh is another distribution function which is used to determine wind speed potential [27]. A special case of the Weibull model is the Rayleigh distribution that usually describes the distribution of wind speed frequencies. The shape factor, k, is known to have a value of 2 for the Rayleigh distribution. As a consequence, the probability density and cumulative distribution functions of the Rayleigh model have been calculated by Eqs. (6) and (7), respectively. The power law equation, as given in Eq. (8), is a simple but useful model of the vertical wind profile, first suggested by Hellman[28], whereby v 1 and v 2 are steady wind speeds simultaneously at elevations and , respectively. The exponent is the Hellmann (or friction) exponent, depending on wind speed, atmospheric stability and the height interval [29]. Average monthly wind speed values of 3, 10 and 50 m were obtained from the NASA Worldwide Energy Resources Prediction (https://power.larc.nasa.gov/) between 2015 and 2019.Therefore, friction exponent was estimated using nonlinear regression analysis as ( = 0.268). Parameter estimates was calculated using SPSS software with correlation coefficients ( = 0.91), as a nonlinear regression analysis. Table 1 Mathematical models used in calculating wind power. No. Definition Formula Mean wind speed and Standard deviation [20,33-35]
1 The monthly mean wind speed (1) 2 The standard deviations of monthly mean (2) wind speed Weibull [5,6,17,21-24,27,34-40] and Rayleigh cumulative distribu tion [23,24,27]
3 Weibull distribution function (3) 4 Weibull cumulative distribution function (4) 5 Gamma function [31,41] (5) 6 Rayleigh distribution function (6) 7 Rayleigh cumulative distribution function (7) The power law 8 The power law by Hellman [19] (8) Calculations of wind power 9 Wind power [17,27] (9) 10 Power based on the Weibull function [27] (10) 11 Power based on the Rayleigh function [27] (11) 12 Capacity factor [30] (12)
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In addition, it is well known that the wind power, P(v), which flows at speed v via the blade sweeping area, A, rises as the cube of its velocity and is defined as shown in Eq. (9). Akpinar and Akpinar [30] defined the monthly or annual density of wind power per unit area of the region on the basis of the probability density function of Weibull, as set out in Eq. (10). For the Rayleigh density function, the density of power has been calculated using Eq. (11) [31,32]. The capacity factor could be calculated using Eq. (12).
3.2. Statistical Indicators In order to compare the measured values with the calculated values and to know how it is close to each other, a selection of statistical indicators was applied. The statistical indicators used in Table 2 include average absolute error, root average square error, average absolute relative error, 95 % uncertainty, root average square relative error, relative root average square error, average absolute bias error, determination coefficient, maximum absolute relative error, and t- statistic. In statistics, the amount of the average absolute error is sometimes used to measure how similar the calculated values become to the measured values. The RMSE is a commonly used indicator for comparing the forecasting errors of various models. Indicator of uncertainty is used to display further information on model deviations. Relative root mean squared error has been deemed excellent when RRMSE < 10%, good if 10% < RRMSE < 20%, fair if 20% < RRMSE < 30%, and poor if RRMSE > 30%. In statistics, the determination coefficient is often used to estimate the models' performance. For the first time, Stone [42] suggested a t-stat indicator that has a long history of common use, to be utilized in conjunction with RMSE and MBE for a more complete assessment of solar radiation estimation models. T-statistics later became a commonly-recognized test to validate whether or not the calculated solar radiation values vary substantially from their measured counterparts. The greater the t-statistic, the more evidence you have that estimated values are significantly different from average. If we know nothing about a population or if you have a limited sample size, t-statistic has been used (< 30). The global performance indicators (GPI) were calculated to determine most suitable wind turbine machine for this location. The GPIs were calculated as the average of all statistical parameters. The coefficient of determination was recalculated as 1-|R2|. Therefore, the lower the statistical parameters, the more accurate the estimate [26].
Table 2 Statistical quantitative indicators, abbreviation, and its equation. No. Statistical Abbreviation Definition Equation indicators 1 Mean absolute MAE The MAE is the sum of absolute values of the error errors divided by the number of observations. 2 Root mean RMSE The RMSE is the root the sum square values of squared error the errors divided by the number of observations. 3 Mean absolute MARE This indicator is expressed as average absolute relative error value of relative differences between estimated and measured data. 4 Uncertainty at U95 Uncertainty with 95% a confidence level where 95% 1.96 is the coverage factor corresponding 95% confidence level, and SD is the standard deviation of the difference between the calculated and measured data. 5 Root mean RMSRE This indicator is used to measure the differences squared relative between values predicted by a model or an error estimator and the values observed.
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6 Relative root RRMSE This indicator is calculated by dividing RMSE mean squared with average value of measured data. error 7 Mean absolute MABE The MBE provides information on the long term bias error performance. A low MBE is desired. A positive value gives the average amount of over estimation in the calculated values. One drawback of this test is that over estimation of an individual observation compensates for under estimation in a separate observation. The MABE gives the absolute value of the bias errors. 2 8 Coefficient of R It depicts the fraction of the calculated values determination that are the closest to the line of measurement data. 9 Maximum erMAX This indicator is expressed as the maximum of absolute relative absolute value of relative differences between error estimated and measured data. 10 t-Statistic t-stat This indicator is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.
4. RESULTS AND DISCUSSION Wind energy is a significant source of energy and is, moreover, called upon to play a key role in the future supply of energy. In this context, the estimation of the potential for wind energy in the Al-Aqiq region, in especially at King Saud Airport, Al-Aqiq City, KSA, is crucial.
4.1. Analysis of Wind Speed Hourly wind data taken from King Saud airport and NASA Worldwide Energy Resources Prediction (https://power.larc.nasa.gov/) from January 1983 to December 2019 were used. In Al-Aqiq, the annual average monthly variations in wind speed are shown in Fig. 4(a). It is obvious that the minimum average wind speed is in November and that the maximum average wind speed is in July, with total values varying from 2.6 to 4.8 m/s per a year, Fig. 4(a). It is observed that the mean wind speed tends to decrease from 1983 to 2019, see Fig. 4(b). The maximum average value occurs in year 1994, with a mean value of 4.2 m/s and the minimum average wind speed value occurs in year 2002 with a mean value of 2.5 m/s, Fig. 4(b). The monthly mean value of the wind speed is ranging from 1.54 m/s in November 2002 to 6.69 m/s in July 2007, Table 3. The overall mean value of the wind speed is 3.39 m/s with a main direction of southwest (average from 1983 to 2019), Table 4. The key wind direction was found to be roughly among east-southeast and south-southwest during all the year except summer months (June-August) it bellows from north-northwest. 8.0 8.0
) 1983-2019 Average s 7.0 /
) Maximum s m ( / 6.0 6.0 Minimum d m ( e 5.0 e d p e s
e 4.0 4.0 p d s n
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g 2.0 Wi a
r 1.0 e 0.0 Av 0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Year (a) Average monthly wind speed during a year. (b) Average yearly wind speed from 1983 to 2019.
Figure 4 Average monthly and yearly wind speed from 1983 to 2019.
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Table 3 Average wind speed from 1983-2019 Wind speed Direction JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Mean (m/s) 1983 4.63 4.12 5.14 4.12 3.60 4.12 5.14 5.14 3.60 3.09 2.57 3.09 4.03 SSW 1984 3.09 3.09 4.12 4.12 3.60 4.12 5.66 4.63 4.12 3.60 3.09 3.60 3.90 SW 1985 3.60 4.12 4.12 3.60 3.09 3.60 4.63 4.63 3.09 3.09 2.57 3.60 3.64 E 1986 2.57 3.09 3.60 4.12 3.60 4.63 5.66 5.14 3.60 3.09 3.09 3.60 3.82 E 1987 3.60 4.12 4.12 3.09 3.60 3.09 4.63 4.63 4.12 3.09 3.09 3.09 3.69 E 1988 3.09 4.12 3.60 3.60 4.12 4.12 5.66 5.66 4.12 3.60 3.09 3.60 4.03 E 1989 4.12 5.14 4.63 3.60 3.09 4.12 5.66 4.63 3.60 3.60 3.09 3.09 4.03 E 1990 3.60 4.12 4.12 3.09 2.57 3.09 4.12 3.60 3.09 3.09 2.57 2.06 3.26 E, SSW 1991 3.60 3.60 4.12 3.60 3.60 4.12 5.14 4.63 3.60 3.60 2.57 3.09 3.77 E 1992 3.60 4.12 3.60 3.09 3.09 4.12 5.14 4.63 3.09 3.09 2.57 3.09 3.60 SSW, E 1993 2.57 4.12 3.09 3.09 3.60 4.12 4.63 5.14 3.60 4.63 3.60 2.57 3.73 SSW, E 1994 3.09 2.57 4.12 3.60 3.09 4.12 6.17 5.66 4.63 4.63 3.60 4.63 4.16 SSW, NNW, E 1995 4.12 4.63 4.12 4.12 3.60 5.14 6.17 5.66 3.60 3.09 2.57 2.06 4.07 SSW 1996 2.06 2.06 2.57 3.60 4.12 4.12 4.12 3.60 2.57 2.06 3.09 2.57 3.04 WSW, NNW 1997 3.09 4.12 3.60 3.09 2.06 2.57 3.09 2.06 2.06 2.57 2.06 2.57 2.74 WSW 1998 4.12 3.60 4.12 3.60 2.57 4.63 5.66 5.14 4.12 3.60 3.09 2.57 3.90 WSW 1999 2.57 2.57 3.60 3.60 4.12 4.12 6.17 5.66 4.12 3.60 3.09 3.09 3.86 E 2000 3.09 2.06 3.60 3.60 3.60 4.63 5.66 4.12 3.60 3.09 2.57 2.57 3.52 WSW 2001 2.57 3.09 3.09 3.09 3.09 3.60 3.60 4.63 3.60 2.57 2.06 2.06 3.09 E 2002 2.57 1.54 2.06 2.06 2.06 3.60 3.09 3.09 3.09 3.09 1.54 2.06 2.49 NNW, E 2003 2.06 2.57 3.09 2.57 1.54 4.12 5.14 4.63 3.09 2.57 2.06 2.57 3.00 SW 2004 2.57 2.57 3.09 2.57 2.57 4.12 4.63 4.63 2.57 2.57 2.06 2.06 3.00 SW 2005 4.63 2.06 2.06 2.57 2.06 3.09 4.63 4.12 3.09 2.06 1.54 1.54 2.79 NNW, SW 2006 2.06 2.57 3.09 2.06 2.06 3.09 4.12 4.63 2.57 2.06 1.54 3.60 2.79 NNW 2007 3.09 2.57 3.09 3.09 2.57 4.12 6.69 4.12 3.60 3.09 2.57 2.06 3.39 NNW, SW, ESE 2008 2.57 3.09 3.09 2.57 2.57 3.60 5.14 4.12 4.12 3.09 2.57 2.06 3.22 NNW, ESE 2009 2.06 2.57 3.09 3.09 3.09 3.60 4.63 4.12 3.60 3.09 2.57 2.57 3.17 NNW, SW 2010 2.57 2.57 3.09 3.09 2.57 2.57 4.63 4.63 3.60 3.09 2.57 2.57 3.13 ESE, NNW 2011 2.57 2.57 3.09 3.09 3.09 4.12 4.63 4.12 3.60 3.60 2.57 2.57 3.30 W, S, E 2012 2.57 3.09 3.09 3.09 3.09 4.12 4.63 4.12 4.12 3.09 2.57 2.06 3.30 E 2013 2.57 3.09 2.57 3.09 3.09 4.63 4.63 4.63 3.60 3.09 3.09 2.57 3.39 E 2014 2.57 2.57 2.57 2.57 2.57 3.09 4.63 4.12 3.60 3.09 2.57 2.57 3.04 E, NW 2015 2.06 2.57 2.57 3.09 3.09 4.12 4.63 4.12 3.60 3.09 2.57 2.57 3.17 E 2016 2.88 4.01 3.60 2.52 2.01 2.78 4.12 2.62 3.50 3.86 3.65 1.80 3.11 SSW 2017 1.90 3.40 4.42 2.06 2.21 2.83 3.76 2.47 4.22 4.11 2.73 4.78 3.24 E 2018 2.83 3.40 2.88 2.83 2.25 3.01 4.37 3.40 3.34 3.09 2.25 2.09 2.98 SSW, ESE 2019 2.78 3.99 4.08 2.75 1.80 3.25 4.00 3.68 4.17 3.72 1.78 2.02 3.17 E
Table 4 Monthly mean value of the wind speed (average from 1983 to 2019). Wind speed Avera JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Max Min (m/s) ge Average 3.0 3.2 3.5 3.1 2.9 3.8 4.8 4.3 3.5 3.2 2.6 2.7 3.4 4.8 2.6 Maximum 4.6 5.1 5.1 4.1 4.1 5.1 6.7 5.7 4.6 4.6 3.7 4.8 4.2 6.7 3.7 Minimum 1.9 1.5 2.1 2.1 1.5 2.6 3.1 2.1 2.1 2.1 1.5 1.5 2.5 3.1 1.5 Direction SSW, S, ESE S, ESE SW SW, NNW NNW NNW ESE ESE SW, S, SSW SW ESE SE ESE Diurnal variance in wind speed offers data on the availability of appropriate winds across the overall 24 hours of the day. In order to research this trend, the total hourly average wind speed values have been shown in Fig. 5. The figure indicates that the wind speed stayed above
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2 m/s all the hours of the day. It remains above 3.0 m/s from 09:00 AM to 10:00 PM and under it for the rest of the day's hours. The average wind speed throughout the entire day ranged from a minimum of roughly 2.1 m/s at 06:00 AM to a maximum of roughly 4.58 m/s at 05:00 PM.
5.0 4.5
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : : : : : : : : : : : : : : : : : : : : : : : 2 0 1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 2 0 1 1 1 1 1 1 1 Hour
Figure 5 Diurnal wind speed (average during year 2014). The Weibull distribution of wind at King Saud airport at Al-Aqiq was derived from windrose analysis using the collected data during year 2014. The percent frequency distribution in the various bins of the average wind speed, which is shown in Table 5. It shows the wind speed stayed above 3.0 m/s for a minimum value of 52.66% in November and a maximum value of 87.95% in July of the time over the entire data collection period. The average wind speed frequency is found to be 64.64%. From the other hand, the speed of wind remained above 4.0 m/s for a minimum value of 29.4% in November and a maximum value of 72.58% in July of the time over the entire data collection period. The average wind speed frequency is found to be 43.81%.
Table 5 Monthly wind speed frequency and calculated power. Frequency (%) Month Above 3.0 m/s Above 4.0 m/s January 64.16 43.48 February 58.17 38.60 March 61.61 41.43 April 57.61 37.99 May 60.88 33.06 June 68.65 48.23 July 87.95 72.58 August 77.07 60.26 September 67.05 49.14 October 58.83 37.54 November 52.66 29.40 December 61.07 34.00 The wind speed data for year 2014 were also analyzed by season. Table 6 summarizes the seasonal changes in wind characteristics in Al-Aqiq city. The speed of the wind remained above 3.0 m/s for almost 61.70%, 62.06%, 77.75% and 56.63% of the time in winter, spring, summer and autumn, respectively. In addition, Table 6 revealed that about 44.70%, 41.03%, 38.89% and 34.50% of the time, wind speed stayed above 4.0 m/s in winter, spring, summer and autumn, respectively. Since several modern wind turbines typically begin to produce more than 2.5-3.0
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m/s of energy, the availability of 65.24 % of wind speed during the year above the cut-in speed of wind turbines is a strong indication that King Saud Airport, Al-Aqiq, is a suitable location for the development of wind farms.
Table 6 Seasonally and yearly wind speed frequency and calculated power. Wind Speed Frequency (%) Bins Year Winter Spring Summer Autumn 0 ≤ N < 1 2.698 4.060 1.966 1.850 3.093 1 < N < 2 10.149 12.927 10.946 4.810 13.028 2 < N < 3 21.903 21.314 25.027 15.541 27.246 3 < N < 4 20.534 20.673 23.167 16.883 22.130 4 < N < 5 17.125 16.613 17.269 17.900 16.538 5 < N < 6 13.624 14.797 11.849 16.374 10.767 6 < N < 7 7.358 7.105 4.782 12.072 4.462 7 < N < 8 3.870 1.816 1.860 8.927 1.904 8 < N < 9 1.540 0.534 1.328 3.423 0.476 9 < N < 10 0.750 0.160 1.275 1.341 0.059 10 < N < 11 0.276 0.000 0.372 0.555 0.119 11 < N < 12 0.118 0.000 0.106 0.185 0.178 12 < N < 13 0.026 0.000 0.053 0.046 0.000 13 < N < 14 0.013 0.000 0.000 0.046 0.000 14 < N < 15 0.000 0.000 0.000 0.000 0.000 15 < N < 16 0.000 0.000 0.000 0.000 0.000 16 < N < 17 0.000 0.000 0.000 0.000 0.000
4.2. Analysis of Weibull and Rayleigh Distributions Monthly average wind speed values and standard deviations have been determined from Eqs. (1) and (2) utilizing the measured data, and time form, k and scale, c, Weibull function parameters have been determined utilizing Eqs. (4) and (5). In Table 7, all measured monthly parameters have been listed by month. The Weibull parameters set out in Table 7 show that the scale factor, c, ranges among 2.20 and 4.50 m/s, whereas the shape factor, k, varies from 1.51 to 2.34. The scale, , Rayleigh function parameter is determined utilizing Eq. (6). The Rayleigh parameter shown in Table 8 reveals that the scale factor, c, ranges from 3.26 and 5.71 m/s.
Table 7 Weibull monthly distribution parameters, estimated using Al-Aqiq city wind speed data (Average during 1983-2019). Parameter Jan Feb Mar Apr May June Jul Aug Sep Oct Nov Dec Max Min Ave c 3.0 2.2 2.8 2.5 2.7 2.8 4.5 3.3 2.9 2.5 2.5 2.7 4.5 2.2 2.867 k 2.157 2.341 1.923 2.116 1.943 2.250 2.013 1.512 1.715 1.994 2.013 1.845 2.341 1.512 1.985 MAE ↓ 0.900 0.991 0.990 0.990 0.990 0.990 0.990 0.989 0.990 0.990 0.990 0.990 0.991 0.9 0.983 RMSE ↓ 0.114 0.154 0.137 0.105 0.148 0.123 0.103 0.099 0.104 0.128 0.137 0.156 0.156 0.099 0.126 MARE ↓ 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.01 0.01 0.010 U95% ↓ 0.267 0.357 0.319 0.252 0.367 0.297 0.247 0.240 0.242 0.314 0.332 0.383 0.383 0.24 0.301 RMSRE ↓ 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.01 0.01 0.010 RRMSE ↓ 0.125 0.154 0.137 0.105 0.148 0.123 0.103 0.099 0.104 0.128 0.137 0.156 0.156 0.099 0.127 MABE ↓ 0.900 0.991 0.990 0.990 0.990 0.990 0.990 0.989 0.990 0.990 0.990 0.990 0.991 0.9 0.983 1-R2 ↓ 0.438 0.665 0.424 0.316 0.177 0.419 0.211 0.189 0.369 0.339 0.254 0.224 0.665 0.177 0.335 erMAX ↓ 0.900 0.991 0.990 0.990 0.990 0.990 0.990 0.989 0.990 0.990 0.990 0.990 0.991 0.9 0.983 t-stat ↓ 0.030 0.027 0.029 0.035 0.030 0.032 0.035 0.036 0.033 0.032 0.030 0.029 0.036 0.027 0.032 ↓ The lower is the better.
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Table 8 Rayleigh monthly distribution parameters, estimated using Al-Aqiq city wind speed data (Average during 1983-2019. Parameter Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Max Min Ave c 4.077 3.26 3.669 5.303 4.077 4.486 5.303 5.712 4.895 4.486 4.077 3.669 5.712 3.26 4.418 MAE ↓ 0.900 0.991 0.990 0.990 0.990 0.990 0.991 0.989 0.990 0.991 0.990 0.990 0.991 0.9 0.983 RMSE ↓ 0.115 0.154 0.138 0.105 0.148 0.124 0.104 0.100 0.105 0.129 0.138 0.157 0.157 0.1 0.126 MARE ↓ 0.010 0.009 0.010 0.010 0.009 0.010 0.009 0.011 0.010 0.012 0.009 0.010 0.012 0.009 0.010 U95% ↓ 0.268 0.359 0.321 0.255 0.370 0.299 0.248 0.242 0.244 0.316 0.335 0.386 0.386 0.242 0.304 RMSRE ↓ 0.010 0.009 0.010 0.010 0.009 0.010 0.010 0.011 0.010 0.015 0.009 0.010 0.015 0.009 0.010 RRMSE ↓ 0.126 0.154 0.138 0.105 0.148 0.124 0.104 0.100 0.105 0.129 0.138 0.157 0.157 0.1 0.127 MABE ↓ 0.900 0.991 0.990 0.990 0.990 0.990 0.991 0.989 0.990 0.991 0.990 0.990 0.991 0.9 0.983 1-R2 ↓ 0.140 0.072 0.120 0.837 0.401 0.348 0.129 0.468 0.465 0.524 0.515 0.309 0.837 0.072 0.361 erMAX ↓ 0.900 0.991 0.990 0.990 0.990 0.990 0.991 0.989 0.990 0.991 0.990 0.990 0.991 0.9 0.983 t-stat ↓ 0.030 0.027 0.029 0.035 0.030 0.032 0.035 0.036 0.033 0.032 0.030 0.029 0.036 0.027 0.032 ↓ The lower is the better. The wind speed data time series are arranged in a frequency distribution format because the format of frequency distribution is more suitable for statistical analysis. Table 9 for the year 2014 shows an example of these data. The frequency at which the wind speed falls within different ranges is displayed in the fourth column of Table 9 (bins). In the fifth, sixth and seventh columns of Table 9, respectively, the potential density distributions determined by the actual functions of Weibull and Rayleigh were presented. The real probability density function and the cumulative probability distributions obtained during 2014 from the calculated hourly time series from Al-Aqiq city are depicted in Fig. 6.
Table 9 Arrangement of data for the daily time-series calculated in the frequency distribution format for the year 2014.
1 0-1 0.5 205 0.0270 2.698 0.6088 3.1491 2 1-2 1.5 771 0.1015 10.149 8.3846 9.1621 3 2-3 2.5 1664 0.2191 21.903 21.5003 14.3621 4 3-4 3.5 1560 0.2054 20.534 21.7615 18.3405 5 4-5 4.5 1301 0.1713 17.125 7.91741 20.8597 6 5-6 5.5 1035 0.1363 13.624 0.79027 21.8726 7 6-7 6.5 559 0.0736 7.358 0.0152 21.5071 8 7-8 7.5 294 0.0387 3.870 0.0000381 20.0238 9 8-9 8.5 117 0.0154 1.540 0.000 17.7587 10 9-10 9.5 57 0.0075 0.750 0.000 15.0630 11 10-11 10.5 21 0.0028 0.276 0.000 12.2535 12 11-12 11.5 9 0.0012 0.118 0.000 9.5794 13 12-13 12.5 2 0.0003 0.026 0.000 7.2079 14 13-14 13.5 1 0.0001 0.013 0.000 5.2261 15 14-15 14.5 0.000 0.0000 0.000 0.000 3.1491 16 15-16 15.5 0.000 0.0000 0.000 0.000 9.1621 17 16-17 16.5 0.000 0.0000 0.000 0.000 14.3621
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Figure 6 Average monthly wind speed during a year (average from 1983 to 2019). Seasonal and yearly analysis of Weibull and Rayleigh parameters are listed in Tables 10 and 11. The parameters of Weibull show that the scale factor c ranges from 2.50 to 3.10 m/s, whereas the shape factor k varies from 1.36 to 2.08, Table 10. The Rayleigh parameter indicates that the scale factor, , ranges from 4.08 and 5.71 m/s, Table 11. The yearly analysis of Weibull and Rayleigh paramet ers showed that the Weibull scale factor, = 2.7 m/s, while the Weibull shape factor, = 1.72 and the Rayleigh parameter, = 5.71 m/s. Table 10 Weibull distributional parameters, calculated using 2014 Al-Aqiq city wind speed data, on a seasonal and annual basis. Parameter Winter Spring Summer Autumn Year Max Min Ave c 2.8 2.6 3.1 2.5 2.7 3.10 2.5 2.750 k 1.936 1.723 1.357 2.077 1.722 2.077 1.357 1.773 MAE ↓ 0.990 0.990 0.990 0.990 0.990 0.99 0.99 0.990 RMSE ↓ 0.126 0.115 0.098 0.122 0.104 0.126 0.098 0.115 MARE ↓ 0.010 0.010 0.010 0.010 0.010 0.01 0.01 0.010 U95% ↓ 0.293 0.285 0.237 0.301 0.257 0.301 0.237 0.279 RMSRE ↓ 0.010 0.010 0.010 0.010 0.010 0.01 0.01 0.010 RRMSE ↓ 0.126 0.115 0.098 0.122 0.104 0.126 0.098 0.115 MABE ↓ 0.990 0.990 0.990 0.990 0.990 0.99 0.99 0.990 1-R2 ↓ 0.368 0.199 0.180 0.273 0.250 0.368 0.18 0.255 erMAX ↓ 0.990 0.990 0.990 0.990 0.990 0.99 0.99 0.990 t-stat ↓ 0.030 0.035 0.036 0.033 0.036 0.036 0.03 0.034 ↓ The lower is the better. Table 11 Rayleigh distributional parameters, calculated using 2014 Al-Aqiq city wind speed data, on a seasonal and annual basis. Parameter Winter Spring Summer Autumn Year Max Min Ave c 4.077 5.303 5.712 4.895 5.712 5.712 4.077 4.997 MAE ↓ 0.990 0.990 0.990 0.990 0.990 0.99 0.99 0.990 RMSE ↓ 0.126 0.116 0.099 0.123 0.105 0.126 0.099 0.116 MARE ↓ 0.010 0.009 0.009 0.008 0.009 0.01 0.008 0.009 U95% ↓ 0.295 0.288 0.239 0.304 0.260 0.304 0.239 0.282 RMSRE ↓ 0.010 0.009 0.009 0.009 0.009 0.01 0.009 0.009 RRMSE ↓ 0.126 0.116 0.099 0.123 0.105 0.126 0.099 0.116 MABE ↓ 0.990 0.990 0.990 0.990 0.990 0.99 0.99 0.990 1-R2 ↓ 0.287 0.754 0.443 0.720 0.762 0.754 0.287 0.551 erMAX ↓ 0.990 0.990 0.990 0.990 0.990 0.99 0.99 0.990 t-stat ↓ 0.030 0.035 0.036 0.033 0.036 0.036 0.03 0.034 ↓ The lower is the better.
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Utilizing the Weibull and Rayleigh probability functions, the wind speed frequency distributions were estimated and the estimates were compared to the probability distribution function measured. The Weibull distribution suits the real distribution data more closely than the Rayleigh distribution, looking only at the graphical outcomes (Fig. 7). The shape, and scale, , Weibull function values were determined using the method referred to in section 3, and the site parameters k and c of 1,72 and 2,70 m/s were analyzed for the average daily in 2014, respectively. The maximum occurrence probability of the site is 21.98 and 21.88 for the Weibull and Rayleigh distributions, respectively.
4.3. Calculation of Wind Energy This section covers the availability of wind in terms of frequency distribution and energy measurements for a selected wind machines. Wind machines were chosen to accommodate a broad range of rated power ranging from 0.40 kW to 600 kW. The diameter of the rotor varied from 1.17 m to 48 m and the cut-in wind speed varied from 1.5 m/s to 3.6 m/s.
(a) Weibull distribution. (b) Rayleigh distribution. (c) Actual, Weibull and Rayleigh distributions.
Figure 7 Wind speed frequency distributions of Al-Aqiq city, KSA. Many wind turbines were chosen for energy measurement purposes. There were a total of 15 wind turbines: Aeronautica Windpower (2), Dewind (1), Enercon (4), Soyut Wind (4), Nordex (2) and SouthWest (2). On the Internet, the technical data and power curves of these machines have been available. Winds turbines of various sizes and manufactured by different manufacturers have been chosen to estimate the potential energy created when installed at Al- Aqiq, KSA. Table 12 summarizes the technical data and requirements for some of the wind turbines chosen. The total annual energy output of wind turbines of various sizes was measured at hub height of 50 m. The power calculation formula in Eq. (9) shows factors which are important for the performance of a wind turbine, with reference to Table 1. It is necessary to sweep the rotor area, A, because the rotor was part of the turbine which captures the energy of the wind. Consequently, the bigger the rotor, the more energy it will capture. The annual production of energy is the best indicator of wind turbine performance. The best way to assess if a specific wind turbine can generate enough electricity to satisfy customer requirements is to calculate the annual energy production from a wind turbine (MWh/Year). A wind energy conversion system's capacity has been obtained by dividing the actual energy generated by the rated power and the number of hours per year, as in Eq. (12). A power curve for a wind turbine will assist in estimating projected output of energy. The estimate was based on the average annual wind speed at the location, the distribution of the wind frequency and the number of hours during the average year in which the wind could blow at each speed. Capacity variables vary from a station's average power: the measure covers the whole length of time, including the whole day, not only the time the turbine is in full operating condition, not only the period it actively generates power.
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Table 12 Main data and specification of the selected wind turbines. Main data Rotor Hub height Wind speeds (m/s) (m) Rated No Type/Model Rotor Number Swept Power powe Typ Cut- diamete of area density Min Max Cut-in Rated r e off r (m) blades (m2 ) (m2/kW) (kW) Aeronautica Windpower 29- 1 225 29 3 Stall 660.5 2.94 30 50 2 14 23 225 Aeronautica Windpower 33- 2 225 33 3 Stall 855.3 3.8 30 50 2 12 23 225 Pitc 3 Dewind D4-600 600 48 3 1809.6 3.02 45 70 2.5 12 19 h Pitc 4 Enercon E30/200 200 30 3 706.9 3.53 36 50 2.5 13 25 h Pitc 5 Enercon E33/330 330 33.4 3 876.2 2.66 37 50 2.5 13 28 h Pitc 6 Enercon E40/500 500 40 3 1256.6 2.51 42 65 2.5 13.5 25 h Pitc 7 Enercon E40/600 600 40 3 1256.6 2.09 NA NA 2.5 13 25 h 8 Soyut Wind 500 500 39.2 3 Stall 1206.9 2.41 50 50 1.5 12.5 24.5 9 Soyut Wind 250 250 41.5 3 Stall 1333.2 5.33 45 45 1.5 12 28 10 Soyut Wind 200 200 36.8 3 Stall 1063.6 5.32 45 45 1.5 12.5 28 11 Soyut Wind 100 100 26 3 Stall 530.9 5.31 40 40 1.5 11.5 26.5 12 Nordex N27/150 150 27 3 Stall 572.6 3.82 30 50 3 13 25 13 Nordex N27/250 250 27 3 Stall 572.6 2.29 30 50 4 16 16.5 14 SouthWest Air X 0.40 1.17 3 NA 1.07 NA 7 35 3.6 12.5 26 15 SouthWest Skystream 3.7 2.60 3.72 3 Stall 10.87 NA NA NA 3.5 13 20
For the 15 turbine models manufactured by Aeronautica Windpower, Dewind, Enercon, Soyut Wind, Nordex and SouthWest, power was calculated. Table 13 lists the estimated power of the various wind turbines. Figure 8 revealed that the highest energy estimation was generated for Dewind D4-600 wind machine, with rates of 1049.72 MWh/Year and capacity factor 19.97%. For Soyut Wind 250 wind machines, the second highest energy estimate was produced with rates of 773.37 MWh/Year and capacity factor 35.31%. The highest capacity factors were calculated for Soyut Wind 250 (773.37 MWh/Year) and Soyut Wind 200 (616.98 MWh/Year) as 35.31%, and 35.22%, respectively. The lowest energy was calculated for SouthWest Skystream 3.7 wind machine, with rates of 0.621 MWh/Year and capacity factors of 17.71%. The second lowest energy and capacity factor were calculated for SouthWest Air X wind machine, with rates of 6.306 MWh/Year and capacity factors of 27.69%, as shown in Fig. 8.
Table 13 Total power/year from wind turbines and capacity factor estimation at hub height of 50 m. No Type/Model Rate Minim Hub height . d um hub 3 m 10 m 50 m powe height Power CF (%) Power CF (%) Power CF (%) r (m) (MWh/Yea (MWh/Ye (MWh/Ye (kW) r) ar) ar) 1 Aeronautica Windpower 225 29 39.902 2.024 105.049 5.330 383.146 19.439 29-225 2 Aeronautica Windpower 225 33 51.671 2.622 136.031 6.902 496.147 25.172 33-225 3 Dewind D4-600 600 48 109.322 2.080 287.808 5.476 1049.722 19.972 4 Enercon E30/200 200 30 42.705 2.438 112.429 6.417 410.062 23.405 5 Enercon E33/330 330 33 52.933 1.831 139.355 4.821 508.271 17.582 6 Enercon E40/500 500 40 75.914 1.733 199.856 4.563 728.935 16.642 7 Enercon E40/600 600 40 75.914 1.444 199.856 3.802 728.935 13.869 8 Soyut Wind 500 500 39 72.912 1.665 191.951 4.382 700.105 15.984
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9 Soyut Wind 250 250 42 80.542 3.678 212.039 9.682 773.370 35.314 10 Soyut Wind 200 200 37 64.255 3.667 169.160 9.655 616.979 35.216 11 Soyut Wind 100 100 26 32.073 3.661 84.437 9.639 307.967 35.156 12 Nordex N27/150 150 27 34.592 2.633 91.069 6.931 332.157 25.278 13 Nordex N27/250 250 27 34.592 1.580 91.069 4.158 332.157 15.167 14 SouthWest Air X 0.40 1.17 0.065 1.845 0.170 4.857 0.621 17.714 15 SouthWest Skystream 3.7 2.60 3.72 0.657 2.883 1.729 7.591 6.306 27.685
1200 40 35 %
1000 ,
r 30 o t
800 c 25 a f
600 y 20 t i c 15 a
400 p
a 10 C 200 5 Power, MW/Year 0 0
Wind turbine machine Wind turbine machine (a) Power generated, MWh/Year. (b) Capacity factors, %.
Figure 8 The power generated and capacity factor for some selected wind turbines.
5. CONCLUSION A monthly time-series of measured wind speed data for the King Saud airport, Al-Aqiq, KSA, was analyzed for a period from 1983 to 2019. In addition, an hourly time-series of measured wind speed data was analyzed for the duration from January 2014 to December 2014. The distributions of power density have been derived and the distributional parameters have been defined. For analysis of the wind energy potential of the site, models of Weibull and Rayleigh were used. The study's most significant outcomes are summarized below. The average wind speed for the Al-Aqiq region, is 3.39 m/s over a 38-year time period with a main direction of southwest. It is evident that the minimum average value for wind speeds occurs in November and that the maximum average value for wind speeds occurs in July, with a total value of between 1,54 and 6,69 m/s per year. The diurnal study showed that the wind speed remains above 3.0 m/s from 09:00 AM to 10:00 PM and below it during the rest of the day's hours. A seasonal analysis reveals that in summer the wind speed is highest (4.41 m/s with a mainly north-northwest direction) and lowest in autumn (2.65 m/s with a mainly east direction). The shape and scale parameters of a Weibull and scale parameters of Rayleigh density distribution functions were calculated for this location. This study concludes that wind data is well represented by the Weibull distribution function as compared to the distribution of Rayleigh density. For 15 wind machines of various sizes generated by Aeronautica Windpower, Dewind, Enercon, Soyut Wind, Nordex and Southwest, the generation of wind energy was considered. The highest capacity factors were calculated for Soyut Wind 250 (773.370 MWh/Year) and Soyut Wind 200 (616.979 MWh/Year) as 35.31%, and 35.22%, respectively. Therefore, the statistical calculations on wind data showed that the location has a good wind potential available.
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NOMENCLATURE rotor sweep area, m2. shape parameter, m/s. CF capacity factor, %.
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