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^{2}

Due to the energy demand and lack of supplied energy of Palestinian cities, wind resource assessment is important and necessary. The objective of the work is to analyze the wind speed data characteristics and wind power potential at eastern Jerusalem that are collected at 10 m above ground level from 2008 to 2018. The variations of monthly, seasonal, and annual wind speed are analyzed, and the measured maximum, minimum, and mean values are presented in this study. Wind speed characteristics have been analyzed by the well-known Weibull distribution function, and used to evaluate the wind power of the proposed site. Moreover, the relationship between wind power and mean wind speed is fitted by a second-order polynomial. The shape parameter moderate values showed that wind speed was relatively steady at the site. The highest average maximum value was found to be 5.7 m/s in June-2008, whereas the mean maximum values ranged from 5.4 m/s in June to 3.8 m/s in November. The highest mean power value was found to be 31.66 w/m
^{2} in July with a maximum value of 23.18 w/m
^{2} in 2013. R
^{2} of the polynomial fit provides values of 95% for monthly mean and 96% for annual mean.

Palestine faces a critical situation with regard to achieving sustainable development. Many problems contributed to the continuous deterioration of the political, economic, social and environmental conditions, and hindered development initiatives. For nearly four decades, the lack of Palestinian infrastructure has impeded any realistic energy progress [

Despite all these challenges, Palestine went ahead with using its natural resources for rehabilitation and construction. Renewable wind energy provides a practical and inexpensive solution to distribute generators of power to vast regions around the world. It has become one of the most convenient and environmentally friendly ways to generate electricity [

Numerous studies in the literature and extensive research interests in recent years have considered the description of wind speed variations by the use of probability density function models. Luna and Church (1974), studied the use of lognormal distribution as a universal distribution of wind speed, however, due to the differences in climate and topography, it was realized that a universal distribution may not be applicable [

Justus et al. (1978) applied the Weibull distribution to study the surface wind speed United States and calculated the power output from wind generation. They found that Weibull was an adequate model and describes well the variations of the wind speed [

Celik in 2003 [

Kitaneh et al. 2012 [

A study by Bassyouni et al. 2015 [

According to Mohammadi et al. 2016 [^{2}.

To sum up, one of the possible solutions to cover the lack of energy in Palestine is generating electricity from wind, however it is necessary for wind power potentials to study wind speed variations at a site. In the present work, the daily values of wind speed of 11 years data were analyzed and used to develop the Weibull distribution model and used to estimate the wind power at a site located in eastern Jerusalem in Palestine. The data were analyzed at the daily, monthly, seasonally and yearly basis, the Weibull parameters were obtained, and the potential of wind power was evaluated for the site.

The energy service in Palestine has become so expensive that it can no longer be afforded by a large portion of the people who are suffering from poverty and scarcity of possibilities. The largest supplier of electricity to the Palestinian electricity sector is Israel Electric Corporation with about 87% of the total consumption, this dependency imposed a different reality in terms of need and efficiency [

Wind speeds in Palestine are moderate [

The city of Jerusalem is located at 31.77˚N 35.22˚E with a height of 780 m above sea level as presented in Map 1. The average annual maximum and minimum air temperature of the study region ranging from 21.0˚ to 11.0˚ Celsius in the year 2018, with higher air temperature in July month and lower air temperature in January.

The daily data of air temperature, atmospheric pressure, and wind speed for 11 years era from January-1-2008 to December-31-2018 recorded by a weather station located at a height of 100 m above the ground level in east Jerusalem were provided by the Palestinian meteorological station's network office. Wind

Map 1. Location of Jerusalem city.

speed data were recorded 8 times a day by a cup generator anemometer. Unfortunately, about 2% of the observed data were missing, this is due to calibration, servicing, and malfunctioning machines.

Wind speed is the main component of wind energy, as the evaluation of wind speed energy in a region depends mainly on the accurate determination of the probability distribution of wind speed values in that region. Previous studies reviewed several distribution functions in order to analyze wind speed, but the two-parameter Weibull distribution was found to be the most simple, accurate and effective [

Several recent studies have been conducted in order to build adequate statistical model that provides an appropriate description of the wind speed distribution. Several models were compared in order to obtain a model that is representative to the experimental wind data [

The general mathematical form of the shape and scale parameters Weibull distribution function can be written as [

f ( v ) = ( k c ) ( v c ) k − 1 exp [ − ( v c ) k ] (1)

Equation (1) expresses the probability F ( v ) as a function of observing wind speed v, the dimensionless Weibull shape parameter k, and the so-called Weibull scale parameter c in units of m/s.

As a consequence, F ( v ) is the cumulative distribution function and can be expressed as [

F ( v ) = 1 − exp [ − ( v c ) k ] (2)

The reasonable fitting of the cumulative distribution function lead to the determination of the Weibull k and c parameters. This can be done by taking the natural logarithm twice of both sides of Equation (2) as expressed in Equation (3)

ln ( − ln [ 1 − F ( v ) ] ) = k ln ( v ) − k ln c (3)

A straight line graph can be obtained plotting ln(−ln[1−F(v)])versus ln(v), the slope of this straight line represents k while the Y-intercept is −klnc. In this work, the Weibull function was fitted to the measured wind speed data by the linear least-square algorithm [

The obtained two-Weibull parameters k and c from Equation (3) are representing a close relation to the mean wind speed value v_{w} as proposed and documented by ref. [

v w = c Γ ( 1 + 1 k ) (4)

where Γ is the gamma function.

The resulted Weibull probability density function based on experimental wind speed data used to calculate the mean power density which is a function of the cube of wind speed as expressed in equation (5):

P = 1 2 ρ v 3 (5)

Equation (6) represents the air density ρ which is a function of air pressure B and temperature T, ρ_{0} = 1.226 kg/m^{3} (density of dry air at standard atmospheric conditions with temperature equal 288 Kelvin and pressure of 760 mm Hg) [

ρ = ρ 0 ( 288 B 760 T ) (6)

In consequence, according to Equation (5), the use of the actual mean wind speed or that obtained from a Weibull fit underestimates the true mean power density, and this will not lead to the correct picture with respect the power density. Due to the highly variance in wind speeds; thus the cube of the average wind speeds is much less as compared the average of the cube wind speed values [

EPF = Mean power density for the month Mean power density at the monthly mean

In similar manner, EPF for the season and annual wind speed data can be calculated. Equation (7) provides more accurate and realistic mean power density.

P = 1 2 ρ ( E P F ) v 3 (7)

The Weibull monthly, seasonally and yearly mean wind speed in this work is used to obtain the mean power density from Equation (7) for the represented period.

In this study, 11 years wind speed data at 10 m height above the ground from January 2008 to December 2018 at eastern Jerusalem, were analyzed at daily, monthly, seasonally and yearly basis. The Weibull function parameters were used to estimate the wind power. Finally, a comparison of the observed versus estimated values of wind speed was conducted.

The following sections are a discussion of the obtained results.

The daily maximum, mean and minimum wind speeds are presented in

The wind speeds of the daily maximum, minimum and mean values were averaged over the period of study and plotted as shown in

The monthly averaged wind speeds are shown for the period along with their mean in

The highest and lowest minimum wind speed values respectively varied from 2.3 to 1 m/s observed in July 2009 and November 2011, whereas the monthly averaged minimum values along the period ranged from 2 m/s in July to 1.2 m/s in November. Overall, the monthly mean values varied from 3.7 m/s in July to

2.5 m/s in November, while highest mean (4.2 m/s) was found in July 2009 and the lowest mean (2.1 m/s) in November 2010.

to November), and winter (December to February). From the results, it was observed that summer seasons are mostly windier. As evident from the monthly average analysis, summer seasons along the period from 2008 to 2018 provides higher average mean wind speeds with a maximum value of 3.9 m/s in 2009, followed by spring seasons. The lowest value was observed to be 2.3 m/s in winter 2014. Overall, winter seasons average mean wind speed values found to be greater than autumn seasons except in 2014 and 2016-2017.

The annual averages of mean wind speed values from 2008 to 20018 were further analyzed and presented in

The monthly average mean wind speed, Weibull parameters, i.e., k, c and v_{w} calculated by Equations (3) and (4), specific wind characteristics ( v a v g 3 , v a v g 3 and EPF), and wind power calculated using Equation (7) of the site for the period (2008-2018) are summarized in

P Wm^{2 } | EPF | (v_{avg})^{3 } obs | v a v g 3 obs | k | c ms^{−1 } | v_{w}_{ } ms^{−1} | v_{obs}_{ } ms^{−1 } | Months |
---|---|---|---|---|---|---|---|---|

18.41 | 1.17 | 21.41 | 25.16 | 2.11 | 3.42 | 3.02 | 3 | Jan. |

14.36 | 1.28 | 16.73 | 21.53 | 1.93 | 3.51 | 2.97 | 2.94 | Feb. |

17.21 | 1.15 | 23.86 | 27.64 | 2.42 | 3.67 | 3.16 | 3.14 | Mar. |

17.53 | 1.13 | 24.12 | 27.33 | 2.03 | 3.63 | 3.05 | 3.1 | Apr. |

19.55 | 1.07 | 27.35 | 29.25 | 2.49 | 3.77 | 3.17 | 3.22 | May |

25.74 | 1.05 | 38.27 | 40.31 | 2.64 | 3.95 | 3.49 | 3.53 | Jun. |

31.66 | 1.02 | 47.11 | 48.31 | 2.78 | 4.12 | 3.61 | 3.66 | Jul. |

26.86 | 1.07 | 37.16 | 39.86 | 2.43 | 3.81 | 3.37 | 3.48 | Aug. |

18.37 | 1.09 | 27.15 | 29.76 | 2.47 | 3.74 | 3.21 | 3.2 | Sept. |

14.22 | 1.15 | 16.14 | 18.63 | 1.88 | 3.44 | 2.74 | 2.72 | Oct. |

10.44 | 1.25 | 11.13 | 13.93 | 1.77 | 3.06 | 2.47 | 2.48 | Nov. |

13.92 | 1.15 | 16.03 | 18.54 | 1.91 | 3.31 | 2.79 | 2.75 | Dec. |

P Wm^{2 } | EPF | (v_{avg})^{3 } obs | v a v g 3 obs | k | c ms^{−1 } | v_{w}_{ } ms^{−1} | v_{obs}_{ } ms^{−1 } | Season |
---|---|---|---|---|---|---|---|---|

18.87 | 1.1 | 25.17 | 27.76 | 2.06 | 3.44 | 3.18 | 3.15 | Spring |

27.63 | 1.06 | 39.24 | 41.83 | 2.11 | 3.71 | 3.61 | 3.55 | Summer |

15.44 | 1.07 | 18.73 | 20.12 | 1.81 | 3.12 | 2.76 | 2.8 | Autumn |

15.94 | 1.06 | 20.92 | 22.31 | 1.93 | 3.22 | 2.95 | 2.9 | Winter |

P Wm^{2 } | EPF | (v_{avg})^{3 } obs | v a v g 3 obs | k | c ms^{−1 } | v_{w}_{ } ms^{−1} | v_{obs}_{ } ms^{−1 } | Months |
---|---|---|---|---|---|---|---|---|

21.16 | 1.09 | 30.14 | 32.83 | 1.82 | 3.67 | 3.28 | 3.25 | 2008 |

25.44 | 1.06 | 35.71 | 38.06 | 1.77 | 3.78 | 3.4 | 3.41 | 2009 |

18.21 | 1.09 | 26.45 | 28.94 | 1.83 | 3.75 | 3.15 | 3.13 | 2010 |

18.25 | 1.1 | 26.31 | 28.92 | 1.96 | 3.73 | 3.15 | 3.14 | 2011 |

18.34 | 1.08 | 26.95 | 29.11 | 1.74 | 3.86 | 3.16 | 3.17 | 2012 |

23.18 | 1.06 | 32.61 | 34.74 | 1.82 | 3.91 | 3.33 | 3.31 | 2013 |

15.76 | 1.08 | 20.13 | 21.88 | 2.01 | 3.41 | 2.91 | 2.87 | 2014 |

16.45 | 1.09 | 22.16 | 24.23 | 1.75 | 3.45 | 2.93 | 2.96 | 2015 |

16.77 | 1.09 | 22.37 | 24.38 | 1.86 | 3.51 | 2.94 | 2.97 | 2016 |

15.83 | 1.1 | 19.87 | 21.93 | 1.79 | 3.67 | 2.92 | 2.88 | 2017 |

18.33 | 1.1 | 24.17 | 26.62 | 1.86 | 3.78 | 3.05 | 3.02 | 2018 |

the maximum k (2.11) in summer and minimum (1.81) in autumn. The values of the shape parameter for the whole dataset were found around 2, which represents that the wind speed was below moderate values at a 10 m height at the candidate site. The average scale parameter in m/s was found to be 3.62 for the monthly mean wind speed, 3.37 for seasonal values and 3.68 for annual basis. The maximum scale parameter values were recorded in July (4.12 m/s), in 2013 (3.91 m/s) and during summer season (3.71 m/s), while the minimum c values were found to be in November (3.06 m/s), in 2015 (3.45 m/s) and during autumn season (3.12 m/s).

To sum up, the values of the shape and scale parameters present seasonal variation and increased at the beginning of the year until reach their maximum values in summer months and then decreased towards the autumn months. The EPF was calculated according to the relation above, it was found that EPF values greater than 1 which indicates that the mean power density for the month, season and year is greater than the mean power density at the monthly, seasonally and annual mean.

The observed (v_{obs}) and estimated (v_{w}) values of the mean wind speed values were compared and presented in Figures 6-8 as well as displayed in Tables 1-3. The Wiebull model underestimates the monthly wind speeds, the maximum observed/Weibull mean wind speed values in m/s are 3.66/3.61 in July, while the minimum values are 2.48/2.47 in November. Seasonally, it was found that Weibull model overestimates the mean wind speeds with a maximum value of observed/Weibull wind speed 3.55/3.61 m/s and was found to be in summer season. The underestimation of monthly values and overestimation of seasonal values are due to the tendency of Weibull distribution, however this distribution is underestimate lower and upper wind speed intervals, while overestimate intermediate wind speed intervals [

overestimates the mean wind speeds in the all the years except 2012-2016 which showed an underestimation of the mean wind speeds. Maximum observed/Weibull mean wind speed 3.31/3.33 m/s was found in 2013, while the minimum values of observed/Weibull mean wind speed 2.87/2.93 m/s was found in 2014.

of determination R^{2} were found to be 95% and 96% for the monthly and annually mean wind speed respectively. _{1} is the coefficient of wind speed and b_{2} is the standard error. The maximum monthly mean wind power was found in July (31.66 w/m^{2}), while the minimum value was found in November (10.44 w/m^{2}), however, July and November months represents respectively the maximum and minimum monthly mean

R^{2} | b_{2} | b_{1} | intercept | Period |
---|---|---|---|---|

95% | 11.41 | 19.41 | 74.92 | Monthly |

96% | 28.71 | −162.66 | 246.34 | Yearly |

wind speed. The maximum/minimum annual mean power 23.18/15.76 w/m^{2} were found in 2013 and 2014 respectively. A seasonal variation of the monthly mean wind power (highest in summer months) was found which indicates that summer season has the maximum mean power with a value of 27.63 w/m^{2}.

In this work, the study of wind speed variation at a site in eastern Jerusalem was conducted in order to have a clear understanding of the energy potential at the site and localized the necessary characteristics of wind parameters. The developed Weibull distribution model from the measured wind speeds was applied to estimate the wind power density. The study was conducted on monthly, seasonal and annual basis. The relation between mean wind power and mean wind speed was fitted by the second-order polynomial function. The highest average maximum values were found to be 5.7 m/s in June 2008, whereas the mean maximum values ranged from 5.4 m/s in June to 3.8 m/s in November. The mean minimum values ranged from 2 m/s in July to 1.2 m/s in November. In general, a seasonal variation of the wind speed values was found with higher values in summer months. The mean wind power was also calculated, the highest mean power value was found to be 31.66 w/m^{2} in July with a maximum value of 23.18 w/m^{2} in 2013. This study benefits from the use of a large dataset and the drawback of this dataset is that they are close to the surface, often located in areas not actually adapted to wind project development. The results can be applied to all studies using surface measurements and could be followed by more precise studies at precise locations at different altitudes above the ground. Further investigations can be done to study whether or not the wind distribution and Weibull parameters vary a lot with the altitude, also, the study of the ability of Weibull distribution and its estimation to cover wind speeds interval frequencies.

The data was provided by the Palestinian meteorological stations network office.

The authors declare no conflicts of interest regarding the publication of this paper.

Alsamamra, H.R. and Shoqeir, J.A.H (2020) Assessment of Wind Power Potential at Eastern-Jerusalem, Palestine Open Journal of Energy Efficiency, 9, 131-149. https://doi.org/10.4236/ojee.2020.94009