Weaknesses and Strengths of Renewable energy in Yemen in Tab. 1 [24] and the renewable energy capabilities in Yemen in Tab. 2 [20].

In 2009, the Government of Yemen approved the national strategy for RE and energy efficiency, aiming to increase 15% of energy efficiency (EE) in the power sector by 2025 [20]. The targeted capacity of RE in total electricity (in MW) by 2025 is shown in Fig. 1.

The Yemeni energy sector consists of oil, natural gas, and biofuels. Energy production in 2012 was «15,109 kiloton of oil equivalent (ktoe) while the consumption was 6,923 ktoe» [20].

The main aspects of literature regarding wind are on wind speed density and functional variations, and they have a wide range of known applications. Some of the functions commonly used to distribute the probability of measured wind velocity at a given location over a given time are the Weibull and Rayleigh distributions. The probability density function for the Weibull distribution is given by Eq. (1) below [23]. (1)f(v)=(kc)(vc)k−1exp[−(vc)k](k>0,v>0,c>1) where f(v) is the probability of observing wind speed; v and k are the dimensionless Weibull shape parameter (k helps in finding how frequently wind speeds are close to some measured speed); c is the Weibull scale parameter with a unit equal to the wind speed unit (k and c characterize the wind potential of the sites under study). The corresponding cumulative probability function of the Weibull distribution is given by Eq. (2). (2)F(v)=1−exp[−(vc)k] The Rayleigh distribution is a special case of the Weibull distribution in which the shape parameter k takes the value 2.0. From Eq. (1) the probability density function for the Rayleigh distribution can be simplified as shown in Eq. (3). (3)f(v)=2vc2exp[−(vc)k] The two parameters of the Weibull distribution are probability functions, k and c, which can be related to the mean wind speed Vm and standard deviation σ as shown in Eqs. (4) and (5) below [23]. (4)k=(σv)−1.086 (5)c=(vmΓ(1+1k)) The Rayleigh distribution shape parameter k takes the value 2.0. From Eq. (1) the probability density function of the Rayleigh distribution can be simplified as shown in Eq. (6). (6)fR(v)=πv2vm2e−π4(vc)2fR(v)=vC2e−v22C2C=vm1.253

The mean value V_m and standard deviation σ of the Weibull distribution can then be computed as shown in Eqs. (7) and (8) [24]. (7)Vm=cΓ(1+1k) (8)σ=c[Γ(1+2k)−Γ2(1+1k)]12 where Γ is the gamma function (standard formula) and using the stirling approximation the gamma function of (x) can be given by Eq. (9) below. (9)Γ(x)=∫0∞ux−1e−udu

The square of the correlation coefficient (R2), chi-square (x2), and root mean square error analysis (RMSE) were used to evaluate the performance of the Weibull and Rayleigh distributions [20]. These parameters can be calculated by Eqs. (10)–(12). (10)R2=∑i=1N⁡(yi−zi)2−∑i=1N⁡(xi−yi)2∑i=1N⁡(yi−zi)2 (11)x2=∑i=1n⁡(yi−xi)2N−n (12)RMSE=[1N∑i=1N⁡(yi−xi)2]12 where y_i is the first measured data, z_i is the mean value, xi is the first predicted data with the Weibull or Rayleigh distribution, N is the number of observations, and n is the number of constants.

The most common equation used for the variation of wind speed with height is the power law expressed as shown in Eq. (13) [9]. (13)v2=v1(h2h1)α where v₁ is the actual wind speed recorded at height h₁ (m), (m/s) and v₂ is the wind speed at the required or extrapolated height h₂ (m), (m/s).

The exponent α depends on the surface roughness and atmospheric stability. Numerically, it lies in the range from 0.05–0.5, with the most frequently adopted value being 0.14, which is widely applicable to low surfaces and well-exposed sites.

It is well known that the power of the wind at speed v (m/s) through a blade sweep area A (m2) increases as the cube of its velocity and is given by Eq. (14) below [16–18]. (14)P(v)=12ρAv3 where ρ (kg/m3) is the mean air density with value of 1.220 kg/m3.

This depends on the altitude, air pressure, and temperature. The expected monthly or annual wind power density per unit area of a site based on the Weibull probability density function can be expressed as shown in Eq. (15). (15)Pw=12ρc3Γ (1+3k) The total wind power density P/A is the total available power per unit area given by Eq. (16). (16)PA=(12ρ1n∑⁡vi3)

where n is the number of days in a month.

Before calculating the average wind power density, vi3 of each day for the extrapolated height at 50 m was calculated (∑⁡vi3) and the values were summed and then divided by the number of days in a month (1n∑⁡vi3).

The electrical energy produced by a turbine over the year is given by the following relationship as shown in Eq. (17) [8]. (17)E=T[12CpρA∫⁡v3f(v)dv] where C_p is the power coefficient. For practical wind turbines, its value is usually in the range of 0 ≤ Cp ≤ 0.4 and T is the time (For the annual wind energy estimation, T = 8,760 h was used).

The available mean wind power density P_d, and the overall wind energy density Ed, of a wind turbine for a period of time T will be calculated as shown in Eqs. (18) and (19) [9]. (18)Pd=PA=12ρv3=0.6125v3 (19)Ed=EA=PdT

Most wind turbines have power curves in their technical notes. This makes it easier to estimate the energy production of any wind turbine when a series of measurements are made at the studied site.

However, sometimes only a probability distribution function may be available. In this case, the wind turbine power output can be expressed as given by Eq. (20) [16]. (20)Pw,avg=∫0+∞⁡Pwf(v).dv where f(v) is the Weibull distribution given by Eq. (1) above, Pw is the electrical power output of the turbine. Fig. 3 expresses the wind turbine electric power/wind speed relationship curve.

Where the curve increases semi-linearly, starting from the cut-in speed vci  (the minimum wind speed at which the turbine starts to rotate) and then stabilizes at the rated wind speed vr necessary for the turbine to generate its rated electrical power P_r, and ends at cut-off speed vco (the wind speed at which the turbine stops generating power). The curve can be divided into two areas, the first is confined between vci and v_r, and the second is confined between vr and v_co. Therefore, the model for electrical power output P_w of the wind turbine is defined as shown in Eq. (21) [17]. (21)Pw=0(v<vci)Pw=Prvk−vcikvrk−vcik(vci<v<vr)Pw=Pr(vr<v<vco)Pw=0(v>vco) Substituting Eqs. (1) and (21) into Eq. (20) yields Eq. (22) [16,17]. (22)Pw,avg=Pr{exp[−(vciC)k]−exp[−(vrC)k](vrC)k−(vciC)k−exp[−(vcoC)k]}

Capacity Factor that was used to choose a suitable wind turbine, is defined as the ratio of average power output P_w,avg to the rated power output P_r as shown in Eq. (23). (23)CF=Pw,avgPr From Eq. (22) above, we can calculate the capacity factor as given by Eq. (24). (24)CF={exp[−(vciC)k]−exp[−(vrC)k](vrC)k−(vciC)k−exp[−(vcoC)k]}

The capacity factor is proportional to C and inversely to k and when fixing the values of C and k, we notice that CF is affected inversely by the difference between the (v_r − v_ci), as it increases as this difference decreases.‏ Since it is normal to choose the turbine with the smallest cut-in speed, on the other hand, one should choose the one with the smallest difference between the two speeds (v_r − v_ci), (in other words, the lowest value of rated speed v_r should be chosen if the cut-in speed vci is the same between two turbines).

The average wind speed of Socotra Island was obtained from the recorded data of the Civil Aviation and Meteorological Authority (CAMA), only for the data available within five years from 2005–2009 (due to the current economical and the political situation of Yemen). The wind rose is a primary source for assessing wind energy due to its brief view of how wind velocity is distributed and how it remains distributed in the desired location according to the area’s topographical influences. Fig. 4 shows the mean wind speed for different month’s indifferent sets of years, and wind rose diagrams are shown in Fig. 5.

Where wind speed increases from February and reaches its peak value in May/June, then, wind speed decreases in July/August, and again rises wind speed in October & decreases gradually till December. Tab. 3 shows the monthly wind speeds in Hodeidah, and the standard deviations calculated from data are available for five years.

As shown in the five years, the average wind speed is 3.36 m/s. The wind speed for the entire year is the maximum monthly value of 4.18 m/s, which arises in February, while the minimum amount is 2.56 m/s that occurs in Sep. The smaller the value standard deviation, the smaller the speed samples are regular.

The wind speed changes with altitude, and actual wind turbines are placed at different lengths, more than 10 meters from the earth’s surface. And to choose the appropriate height for the wind turbines, the average monthly and annual wind speeds are calculated at different heights (10, 30, and 50 m) using Eq. (9). This is the first step to using this data to calculate and evaluate wind power within the specified location. At these heights, the annual average of wind speed became 8 m/s at 10 m, 12.3 m/s at 30 m, and 15.2 m/s at 50 m, respectively, as shown in Figs. 6 and 7.

The variation of wind speeds is often described using the Weibull density function. It is a widely accepted statistical tool for evaluation of local wind probabilities and is considered as a standard approach. Eqs. (4) and (5) above were used to calculate the Weibull parameters for the available data, and the results are presented in Tab. 4.

As shows, yearly Weibull parameters and average Weibull parameters for the whole five years, from the table, while scale parameters vary between 3.14 (2005) and 4.05 (2009), the shape parameters range from 3.46 (2005) to 4.35 (2007). The five years’ average value of scale and shape parameters are 2.78 and 2.97, respectively.

There are many distribution functions to describe the wind speed frequency curve. In this study, Weibull functions were the most widely used and accepted in the specialized research journal. Yearly wind speed probability density and cumulative probability distributions derived from the measured data of Hodeidah for whole years are shown in Fig. 8.

The Weibull approximation of the probability density distribution of wind speeds for the whole years is shown in Fig. 9.

The monthly wind speed probability density distribution derived from the measured data of Hodeidah for whole years are shown in Fig. 10.

The monthly wind speed cumulative probability distribution derived from the measured data of Hodeidah for whole years are shown in Fig. 11.

The Weibull probability density distributions for each of the five years were analyzed. The distributions obtained are illustrated in Fig.12.

The results shown in Figs. 10–12 show that all curves have a similar tendency to wind speed for cumulative density and probability density. The annual probability density distribution obtained from the Weibull model were compared with measured data distributions to study their suitability. The yearly comparison of Study Location shows that the Weibull model corresponds to the distribution of the probability density of metric data as illustrated in Fig. 9 above.

To calculate the average monthly wind power per unit of the cross-section of the turbine, where the air density of 1.225 kg/m³ energy density is calculated at different heights: 10 m, 30 m and 50 m as shown in Tab. 5 and Fig. 13.

A slight difference in wind speed will result in a massive difference in the density of wind energy because the wind power density is proportional to the wind speed cube. This calculated wind energy was estimated, based on these calculated wind power estimates, for different wind categories based on the international wind energy classification, as shown in Tab. 6.

According to the standard of international wind power classification, the Hodeidah area falls under class 2 and is classified as ‘Marginal’ for most of the year. It has an average wind power density of 173.5 W/m2 at 50 m height and an average wind speed of 6.4 m/s at 50 m height, which means that the site is not considered suitable for electric wind on a large scale. It is sufficient for electrical and mechanical applications not connected to networks, such as wind generators, battery charging, water pumping, and agricultural applications.

Using Eqs. (17) and (18) above, we can calculate the average of monthly and annually wind energy per unit of the cross-section of the turbine. Thus, the wind energy of Hodeidah was estimated at different heights: 10, 30, and 50 m, as shown in Fig. 14.

Since wind energy is proportional to the height of the axis, the average annual wind energy density is 220.8 KWh/m2/year at 10 m, 822.6 KWh/m2/year at 30 m 1519.9 KWh/m2/year at 50 m, respectively.