Evaluation of Weibull parameters for wind energy analysis in the eastern region of the Kingdom of Morocco

Abstract

This document delves into evaluating wind power potential within Morocco’s Oriental region, encompassing an extensive study of 23 locations over 43 years. The analysis was conducted using the advanced MERRA2 data reanalysis system coupled with MATLAB software. Our comprehensive study aims to map the wind energy capabilities across these sites. We employed eight distinct algorithms to adapt the Weibull distribution for the wind speed data. Additionally, the research includes an analysis of the wind rose and assesses the Capacity Factor ( $CF$ ) to determine the most efficient periods for wind energy production. Our findings highlight that sites S4, S7, and S11 create an ideal geographic formation for wind farm placement. Within this formation, site S8, boasting a ( $CF$ ) of 36.97%, emerges as a critical location, especially when paired with the EWT DW54 500 wind turbine model. This investigation opens new avenues for advancing wind energy in the region.

Keywords

Wind energy Weibull distribution algorithm capacity factor power density

Introduction

The growing importance of renewable energies over fossil fuels is evident worldwide due to their many environmental and economic benefits. This transition to renewable energies has been widely recognized and supported by organizations such as the International Energy Agency (IEA, 2023). In 2020, renewables accounted for almost 29% of global electricity generation, while fossil fuels accounted for around 63%. However, the trend shows a significant shift toward renewables.

Wind power’s contribution to global electricity generation is expected to rise from 5% to 30% by 2050 (Farina and Anctil, 2022). For example, since 2000, the United States has increased its wind energy (WE) production capacity by an average of 22.6% per year, according to Renewable Energy Capacity Statistics data (IREA, 2021). This impressive growth testifies to the United States’ commitment to (WE) and its desire to transition to more sustainable energy sources. Moreover, this trend aligns with the significant advances in (WE) supported by research and innovation initiatives such as those led by Energy Science and Innovation (Energy, 2023). Total wind power capacity is expected to reach 224 GW in 2030 and 404 GW in 2050 (Can Sener et al., 2023).

In 2019, China led globally in newly installed (WE) capacity, reaching 26 gigawatts (GW) and achieving a total capacity of 236 GW. Despite this, (WE) comprised only 5.9% of China’s unlimited electricity usage (Gao et al., 2022; Shi, 2011). Meanwhile, India ranked as the world’s fourth largest wind power producer, adding 3.61 GW that year. India’s cumulative wind power capacity surpassed 31 GW, making up 6.6% of the global market. Furthermore, India’s share in the worldwide installed (WE) capacity stood at approximately 9.1%. (Kumar and Sawyer, 2016; Sawyer and Dyrholm, 2016).

The benefits of this transition are clear: reduced greenhouse gas emissions, improved air quality, diversification of energy supply sources, and even job creation (Mert et al., 2016).

Historically, Morocco has heavily depended on fossil fuels, particularly oil and coal, to meet its energy needs, resulting in high import costs, and vulnerability to international price fluctuations. The graph below (Figure 1) shows the total amount of non-renewable and renewable energy consumed by the Kingdom of Morocco over 30 years (IEAMCR, 2023).

Figure 1.

Total energy supply in Morocco 1990–2020.

The Kingdom has made significant progress in managing its growing energy demand by adopting a diversified energy strategy and increasing its share of renewable energies. This energy transition aims to meet electricity needs while preserving the environment and stimulating economic growth. Between 2009 and 2022, electricity demand in Morocco grew by an average of 4.12% per year, driven mainly by the electrification of rural areas, economic growth, and the expansion of the infrastructure, industry, agriculture, tourism, and social housing sectors (NOEW, 2023). This strategy has been crowned with success, restoring the balance between electricity supply and demand, and increasing the share of renewable energies to more than 52% by 2030 (Taoufik and Fekri, 2021).

Morocco has taken significant steps to diversify its energy sources in pursuit of greater energy independence, gradually moving away from imported fossil fuels. In addition to focusing on solar and hydroelectric power, the country has also turned to other renewable energy sources, such as biomass and wind. By 2022, (WE) projects had been developed in 5 of the 12 regions of the kingdom. Among these, the Tangier-Tetouan region stands out with an installed capacity of 512 MW, accounting for 24% of the national total. This is followed by the Fes-Meknes region with 87 MW (4%), the Marrakech-Safi region with 96 MW (4.5%), the Draa-Tafilalt region with 210 MW (9.5%), and finally the Laayoune Sakia EL Hamra region, which holds the largest installed capacity of 1254 MW, or 58% of the total. Table 1 presents statistics relating to three forms of energy up to 2022 (METSDDET, 2023).

Table 1.

Distribution of energy production capacities.

	Wind	Solar	Hydroelectric	Total
Installed capacity	1460 MW	830 MW	1771 MW	4031 MW
Share of energy in total installed capacity (%)	13.48	7.82	16.70	38

Morocco’s transition to renewable energy sources necessitates close collaboration with international partners to finance and develop clean energy projects. The hosting of COP22 in Marrakech in 2016 strongly demonstrated the country’s commitment to climate change mitigation. Morocco aims to become a significant exporter of green electricity by harnessing its solar and (WE) potential. A notable project in this regard was initiated in the Guelmim-Oued Noun region in 2021. This project involves installing solar and wind installations and battery storage, with a production capacity estimated at around 10.5 GW (Daoudi et al., 2022; Xlinks, 2021).

The Global Wind Energy Council (GWEC, 2023) indicates that Morocco will substantially enhance its (WE) output. The country’s target is to expand its wind power capacity by 1.8 GW by 2026, including an intermediate objective of achieving an additional 1 GW by 2024. This ambition forms a key component of Morocco’s more comprehensive plan to launch new (WE) developments in different regions beginning in 2023.

Regions like Tangier-Tetouan, Marrakech-Safi, Fes-Meknes, and Laayoune-Sakia El Hamra are gearing up to enhance their (WE) output, planning capacity expansions ranging from 63 MW to 450 MW. Furthermore, areas such as Guelmim Oued Noun and Dakhla Oued Eddahab are preparing to establish new wind farms, with projected 80 MW and 190 MW capacities, respectively. These initiatives are pivotal in Morocco’s energy strategy, highlighting the country’s commitment to more sustainable and environmentally friendly energy production. Our study focuses on the Oriental region, which has garnered attention from government decision-makers and experts for the potential installation of a wind farm. Preliminary studies are underway to assess feasibility and lay the groundwork for future (WE) developments in this region.

Literature review

(WE) potential has gained significant attention in renewable energy research. This review delves into past and current studies on the subject:

Bharani and Sivaprakasam (2022) study evaluated (WE) prospects at five specific sites (S1–S5) in Tamil Nadu, India. Data from 2016, gathered at 100 meters above sea level, were analyzed using the Weibull distribution model. The findings suggest that sites S1, S2, and S3 are suitable for wind turbine installation.

Mohamadi et al. (2021) investigated (WE) potential across 22 areas in eastern Iran, considering wind speed (WS), wind power density, and the Weibull distribution. They discovered that the average (WS) exceeded 4 m/s at all sites, with ten sites recording speeds of 5 m/s. The study also found that the Mapna 2.5 MW and Vestas V100-1.8 MW 60 turbines outperformed others regarding annual energy yield and cost efficiency.

Gil Ruiz et al. (2021) research focused on the Caribbean region of Colombia, assessing wind potential through 10-minute average (WS) data from 13 weather stations and comparing it with ERA5 reanalysis data for wind farm development. The study highlighted average (WS) between 2.2 and 8.3 m/s, with several sites exhibiting wind power densities above 800 W/m² and capacity factors nearing 50%, comparable to the world’s most efficient wind farms.

El Khchine and Sriti (2021) investigated the potential for (WE) along the coast of Morocco, focusing on regions including Al Hoceima, Boujdour, Essaouira, Laayoune, and Tantan. They analyzed (WS) and direction data, recorded hourly over a four-year period. This data was used to compute wind power and energy densities monthly and annually at different mast heights using the Weibull distribution method. Their findings indicated that (WS) were higher in the northern coastal areas during winter and southern areas during summer, with the highest power densities observed in some areas in July.

Overview of the energy mix

Our study focuses on the Oriental region of Morocco, which, with a population of 2.3 million and an area of 90,127 km², showcases various renewable energy projects. These projects, listed in Table 2 (RICOR, 2020), include those already operational, accounting for about 52% of the total energy capacity of the region and projects under development, making up the remaining 48%. It is noteworthy that (WE) occupies a marginal share (0.4%) in the region’s energy landscape. This observation leads us to question the wind potential of the Oriental region, aiming to enhance the presence of this energy source in the local energy mix.

Table 2.

Renewable energy projects in Eastern Morocco—Installed and under development.

Location	Type of RE	Technology	Installed capacity
Projects in operation
Ain Bni Mathar	Thermal-solar	CSP/PV	472 MW
Oujda	Waste treatment and valorization	Biogas extraction and biomethane	2.3 MW
Saidia-Oujda	Public lighting	Photovoltaic (PV)	2.3 MW
Nador-Barrage Mohamed V	Hydroelectric	Hydroelectric	23 MW
Total			499.6 MW
Projects under development
Ain Beni Mathar	Solar	Photovoltaic (PV)	20 MW
Bouanane	Solar	Photovoltaic (PV)	20 MW
Maroc Ain Beni Mathar	Solar	Photovoltaic (PV)	150 MW
Guercif	Solar	Photovoltaic (PV)	100 MW
Nador	Solar-wind	Photovoltaic (PV)	1.95 MW
Figuig-Centrale Nova Power Energy	Solar	Photovoltaic (PV)	20 MW
Ain Beni Mathar-Centrale DIACORP Energy	Solar	Photovoltaic (PV)	150 MW
Total			461.95 MW

In the absence of in-depth studies focused on the Oriental region of Morocco, our research aims to clarify the theoretical perspectives and estimate the potential of this region in contributing to the energy transition toward cleaner and renewable sources. We investigate the role that the Oriental could play in Morocco’s strategy toward sustainable energy, as well as the theoretical projections of its capacity to generate (WE) efficiently. This inquiry arises in a context where precise knowledge of the wind potential in this region remains limited, underscoring the vital importance of our study in addressing this information gap.

In the following sections of this document, we will detail the adopted methodology (Section 4), descriptive statistics (Section 5), and the application of various algorithms to determine the shape ( $k$ ) and scale ( $c$ ) factors of the Weibull distribution (Section 6). The statistical analysis will be presented in Section 7, and the results obtained will be discussed in Section 8. We will conclude with a final section dedicated to the conclusion of our study.

Methodology

This research aims to evaluate the potential for (WE) in the Oriental region of Morocco, concentrating on 23 distinct locations. The methodology involves analyzing MERRA2 reanalysis data spanning 43 years, from January 1, 1980, to December 31, 2022. Significant advances in computer hardware and software performance have greatly improved our ability to perform statistical data analysis, as highlighted by Schlotter (2013). MATLAB and WRPLOT software will be our leading platforms for this evaluation. Figure 2 illustrates the adopted methodology.

Figure 2.

Diagram of the methodology for the study of wind energy potential in the eastern region.

Data collection will begin with the extraction of MERRA2 reanalysis data for the Oriental region. This data will then be subjected to pre-processing to eliminate errors and missing values, thus ensuring the quality of the data for subsequent analysis.

The first step in the analysis will be to perform descriptive statistics on the data. Parameters such as mean wind speed (MWS), dominant wind direction, standard deviations, and other relevant statistics will be calculated for each location.

Subsequently, a Weibull distribution analysis will be undertaken using eight different algorithms, including the maximum likelihood and Lysen’s methods, to fit the Weibull distribution to the (WS) data. The best fit will be selected for each location.

The analysis will continue with a monthly and daily wind assessment. The monthly (WS) profiles will be used to identify periods of strong or weak wind, while the analysis of daily variations will be used to identify peak wind hours.

Finally, determining the most favorable locations will be based on calculating the capacity factor for each site, using (WS) data and the specific power of the wind turbines. In addition, the estimated energy output for each location will be used to rank the sites according to their (WE) potential.

ArcMap software will be used for visualization and mapping for clear communication of the results. Thematic maps will be created to graphically represent the most favorable locations regarding (WE) potential, considering capacity factor, and output energy data. Appropriate legends, scales and titles will be included to interpret the maps effectively. Figure 3 illustrates the studied locations and the position of the Oriental region on the map of Morocco.

Figure 3.

Locations studied in the eastern region of Morocco.

This approach offers a robust framework for assessing (WE) potential in Morocco’s Oriental region. By leveraging MERRA2 reanalysis data, advanced software tools, and thorough examination of wind characteristics, it aims to pinpoint optimal sites for wind farm construction.

Descriptive statistics

Applications and interpretations in descriptive statistics

Table 3 presents detailed information for each of the 16 chosen weather stations. It includes the station’s name and assigned reference number. At a height of 50 m above ground level, it lists various (WS) metrics: average, variance, minimum and maximum speeds, asymmetry coefficient, kurtosis coefficient, average cubic (WS), median, and mode.

Table 3.

Wind speed statistics at 50 m height for 16 selected weather stations.

Station (50 m)	Vm	Var	Sk	Kr	CV
S1	5.673	7.823	0.461	0.153	49.298
S2	5.646	7.318	0.679	0.801	47.914
S3	5.960	7.655	0.528	0.483	46.424
S4	6.008	8.194	0.384	0.082	47.647
S5	5.926	8.146	0.507	0.377	48.168
S6	5.450	7.123	0.691	0.829	48.974
S7	6.249	8.276	0.498	0.489	46.035
S8	6.297	8.369	0.488	0.523	45.941
S9	5.996	7.873	0.538	0.556	46.798
S10	5.847	8.291	0.592	0.524	49.244
S11	6.083	9.441	0.602	0.366	50.513
S12	5.444	7.652	0.693	0.587	50.815
S13	5.545	7.314	0.622	0.732	48.772
S14	5.597	8.270	0.680	0.582	51.379
S15	5.042	6.984	0.778	0.700	52.414
S16	4.662	6.393	1.157	2.231	54.237
S17	5.176	7.027	0.783	0.921	51.210
S18	4.887	6.496	0.775	0.853	52.152
S19	4.571	6.503	0.782	0.808	55.786
S20	4.578	7.172	1.213	2.432	58.502
S21	4.935	6.603	0.800	0.916	52.073
S22	4.688	6.290	0.895	1.327	53.495
S23	4.492	6.027	1.362	2.915	54.655

Eshete and Abate (2022) conducted a theoretical study over 4 years in Nifas Mewucha, Amhara province, Ethiopia, focusing on assessing wind power potential using wind speed as a critical indicator. Our research, evaluating wind power potential in the Oriental region of Morocco, relies on data from ten wind stations, designated as S1, S3, S4, S5, S7, S8, S9, S10, S11, and S14. This data reveals average wind speeds (MWS) ranging from 5.597 to 6.297 m/s, thus highlighting the region’s diversity of wind speed profiles. The variances, ranging from 7.655 to 9.441, demonstrate data variability from one station to another. The skewness measures, fluctuating between 0.384 and 0.680, indicate a slight rightward skew in the distribution of wind speeds. Kurtosis values, varying from 0.082 to 0.556, suggest a slightly less peaked distribution than average. Moreover, the coefficient of variation percentage (CV%) is notably high, reaching up to 51.379%, emphasizing the significant variability of wind speeds among different stations. Continuing our study, we delve deeper into this analysis by examining the minimum, maximum, median, Q1, and Q3 quartiles through a box plot diagram. This more detailed analysis will enhance the understanding of the region’s wind power potential and aid in more effective planning of wind farms.

Figure 4 presents a crucial analysis of (WS) frequency at ten selected stations from the initial 23, using a 0.5 m/s interval. This selection of stations is informed by NREL Table 4, as cited in El Hadri et al. (2019) study, which is a well-regarded source in renewable energy research. This analysis plays a significant role in understanding the wind potential at these locations.

Figure 4.

The wind speed frequency for the 10 selected stations.

Table 4.

Classes of wind speed.

Height: 50 m	1	2	3	4	5	6	7
	Poor	Marginal	Fair	Good	Good	Excellent	Superb
$v_{m}$ (m/s)	<5.6	5.6–6.4	6.4–7	7.0–7.5	7.5–8.0	8.0–8.8	>8.8

This analysis identifies the most common and least common speed ranges, providing crucial information for designing efficient wind farms and managing the electricity grid. It also helps to assess the reliability of (WE) supply and anticipate seasonal and diurnal variations, contributing to more accurate energy planning and the stable integration of (WE) into the regional energy mix.

Whisker box

Whisker boxes were first proposed by statistician Tukey (1977) and are powerful graphical representations of data that provide an overview and numerical summary of a data set (Figure 5).

Figure 5.

Visualization of a box-and-whisker plot: unveiling vital data statistics.

The box plot is an essential tool in our study of (WS) across the 23 weather stations. Each box plot illustrates the distribution of (WS) at a specific station, presenting crucial information such as the median, quartiles, and interquartile range. Outliers are removed from the diagram (Moeini et al., 2021).

By observing these diagrams in parallel for the 10 stations (Figure 6), we can quickly identify variations and trends between the different localities. Whisker boxes also allow us to assess the data dispersion, detect extreme values, and observe the symmetry or asymmetry of the distribution.

Figure 6.

Comparative analysis of wind characteristics across 10 meteorological stations using box-and-whisker plots.

Weibull statistics

As distinct from other renewable sources like solar or tidal power, (WE) is dispersed and varies in its flow. A deep understanding and characterization of (WS) variation in each location is crucial for harnessing (WE) effectively. This knowledge is vital for developing efficient (WE) conversion technologies (Signe et al., 2019).

Various density functions have been investigated to model (WS) frequencies, including the three- or two-parameter Weibull distribution (Deep et al., 2020), the Rayleigh distribution, the two-parameter lognormal, inverse Gaussian, and gamma distributions (Sohoni et al., 2016). The two-parameter Weibull distribution has recently garnered significant attention due to its adaptability and straightforwardness in accurately fitting empirical data. Moreover, once this distribution is established for (WS) at a certain height, it can be extended to different altitudes, facilitating the assessment of wind potential in diverse regions.

Distribution function: Probability and cumulative

The Weibull distribution function $f (v)$ with two parameters $k$ (form) and $c$ (scale) is given by the following formula (van Vuuren and Vermeulen, 2019):

f (v) = \frac{k}{v} {(\frac{v}{c})}^{k - 1} e^{- {(\frac{v}{c})}^{k}}

(1)

Where $v$ is the (WS)

The cumulative function noted $F (v)$ is called the cumulative distribution function, which shows the integration and accumulation of the relative frequency for each speed interval. It is presented as follows:

F (v) = 1 - e^{- {(\frac{v}{c})}^{k}}

(2)

Wind power density

The wind power density quantifies the efficiency with which (WE) can be converted into usable energy (Manwell et al., 2009). It represents the amount of (WE) available per unit area and time and is in the following form:

P_{wind} (v) = \frac{1}{2} ρ S v^{3}

(3)

Where $P_{wind} (v)$ is the potential wind power density as a function of (WS) $(v)$ , $(S)$ is the area swept by a wind turbine, and $(ρ)$ is the air density of 1.225 kg/m³.

Study algorithm

Empirical methods rely on observation and experimentation to collect data, providing solid evidence to test hypotheses. They provide reliable data to establish causal relationships and improve understanding of underlying processes. These algorithms include:

Empirical algorithm of Jestus (EAJ)

The EAJ algorithm suggested in 1977 uses the (MWS) ( $v$ ) and standard deviation ( $σ$ ) to determine the parameters of shape $(k$ ) and scale $(c$ ) using the following formulae (Baqir et al., 2023):

k = {(\frac{\bar{v}}{σ})}^{1.086}

(4)

c = \frac{\bar{v}}{Γ (1 + \frac{1}{k})}

(5)

where $(Γ)$ refers to the gamma function.

Energy patern factor algorithm (EPFA)

This algorithm enables (WS) data to be analyzed, providing information on the temporal variations of the wind. The following mathematical equation calculates k and c once the energy factor $(E_{PF})$ is determined (Carneiro et al., 2016):

E_{PF} = \frac{\frac{1}{n} \sum_{1}^{n} v_{i}^{3}}{{(\frac{1}{n} \sum_{1}^{n} v_{i})}^{3}}

(6)

k = \frac{1}{3.9557 E_{PF}^{0.898}}

(7)

c = {(\frac{1}{n} \sum_{1}^{n} v_{i}^{k})}^{\frac{1}{k}}

(8)

Empirical algorithm of Lysen (EAL)

Similar to the empirical method of Lysen, the parameter $(c)$ is calculated according to equation (Aziz et al., 2023):

c = \bar{v} {(0.568 + \frac{0.433}{k})}^{- \frac{1}{k}}

(9)

The $(k)$ factor is like equation (4).

Mabchour algorithm (MA)

Known as the Moroccan Algorithm, this method has been used to evaluate the wind potential in the Kingdom. The values of $(k)$ and $(c)$ are calculated using the following equations (Kang et al., 2021):

k = 1 + (0.483 \times (\bar{v} - 2))^{0.51}

(10)

c = \frac{\bar{v}}{Γ (1 + \frac{1}{k})}

(11)

Maximum likelihood algorithm (MLA)

The MLA, an iterative statistical approach, is employed for estimating the parameters of a probability distribution in a data set and predicting (WS) at a specific site. The shape parameter ( $k$ ) and scale parameter ( $c$ ) are derived using the following equations (Liu et al., 2023):

k = {[\frac{\sum_{i = 1}^{N} v_{i}^{k} \ln (v_{i})}{\sum_{i = 1}^{N} v_{i}^{k}} - \frac{\sum_{i = 1}^{N} \ln (v_{i})}{N}]}^{- 1}

(12)

c = {[\frac{1}{N} \sum_{i = 1}^{N} v_{i}^{k}]}^{1 / k}

(13)

Graphical algorithm (GA)

The GA algorithm allows the fitting of a straight line to the actual wind data. The time series data representing (WS) must be arranged in ascending order. GA is based on the following relationship, which can be obtained by taking the double natural logarithm of the Weibull cumulative distribution function, as described in (Vu and Tran, 2023):

\ln [- \ln (1 - F (v))] = kln (v) - kln (c)

(14)

Using the two equations $x$ and $y$ : $y = \ln [- \ln (1 - F (v)]$ and $x = \ln (v)$ , a straight line can be obtained and fitted to the data using linear regression. Then, the shape parameter can be calculated from the slope of this line, while the scale parameter can be determined based on the point of intersection of the line with the vertical axis (the $y$ -axis).

WAsP algorithm (WAsP.A)

WAsP.A distinguishes itself from other algorithms by incorporating air movement and the atmospheric layer in direct contact with the Earth’s surface. This approach facilitates accurate long-term predictions of (WS) and direction at specific sites. WAsP.A considers the intricate topographical and meteorological factors that influence wind patterns, merging detailed field data with statistical models of wind flow. This results in highly precise forecasts of (WE) resources and energy production potential (Baseer et al., 2017; El Khchine et al., 2019).

X = 1 - F (v)

(15)

In this context, ( $X$ ) symbolizes the proportional values corresponding to observed (WS) that exceed the average (WS). The cumulative distribution function $F (v)$ is used to estimate the proportional values less than v, whereas $1 - F (v)$ computes the proportions greater than $v$ . The (MWS) is expressed in equation (11). To adhere to the second WAsP.A criterion, equation (11), is integrated into equation (2), leading to the derivation of the subsequent equation:

X = \exp [- Γ {(1 + \frac{1}{k})}^{k}]

(16)

which can be expressed as follows:

- \ln (X) = - Γ {(1 + \frac{1}{k})}^{k}

(17)

when using the WAsP.A method to fit the Weibull distribution function, the Windographer software determined the values of X and iteratively solved equation (17) using Brent’s method to calculate the (WS) at constant speed (Khan et al., 2023).

Openwind algorithm (OA)

Openwind uses a Weibull distribution fitting algorithm to ensure that the mean wind power density and (MWS) match the observed data, thus improving the accuracy of wind forecasts (Lambert, 2017; Wang et al., 2016). Two assumptions to consider, the first is:

P_{Weibull} = P_{Obs}

(18)

This means that:

\frac{1}{2} ρ c^{3} Γ (1 + \frac{3}{k}) = \frac{1}{2 N} ρ \sum_{1}^{N} v_{i}^{3}

(19)

The form of the scale factor is therefore:

c = \sqrt[3]{\frac{\frac{1}{N} \sum_{i = 1}^{N} v_{i}^{3}}{Γ (1 + \frac{3}{k})}}

(20)

The second assumption is:

{\bar{v}}_{Weibull} = {\bar{v}}_{Obs}

(21)

This means that:

c Γ (1 + \frac{1}{k}) = \frac{1}{N} \sum_{1}^{N} v_{i}

(22)

The 2nd scaling factor becomes:

c = \frac{\frac{1}{N} \sum_{i = 1}^{N} v_{i}}{Γ (1 + \frac{1}{k})}

(23)

The equation containing the unknown k is as follows:

\sqrt[3]{\frac{\frac{1}{N} \sum_{i = 1}^{N} v_{i}^{3}}{Γ (1 + \frac{3}{k})}} = \frac{\frac{1}{N} \sum_{i = 1}^{N} v_{i}}{Γ (1 + \frac{1}{k})}

(24)

In applying Openwind’s Weibull fitting algorithm, Windographer first solves equation (24) iteratively using Brent’s method to determine the parameter $(k)$ is value. It then uses equation (20) to calculate the parameter ( $c$ ).

Statistical analysis

Several statistical measures have been suggested for assessing the effectiveness of the eight algorithms mentioned above in estimating the Weibull distribution parameters. Key statistical indicators used in this context are the coefficient of determination (R²), the root mean square error (RMSE), and the mean percentage error rate (MAPE). These metrics are commonly employed to evaluate the accuracy of data fitting. The equations are outlined below (Mohammadi et al., 2016; Tonsie Djiela et al., 2020):

R^{2} = 1 - \frac{\sum_{i = 1}^{n} {(y_{i} - x_{i})}^{2}}{\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2}}

(25)

RMSE = {[\frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - x_{i})}^{2}]}^{0.5}

(26)

MAPE = \sum_{i = 1}^{N} \frac{x - y}{x}

(27)

Results and discussion

Wind conditions at selected stations

Wind rose

The wind rose diagram serves as an instrument for illustrating the frequency of diverse (WS)s and their respective directions. It offers a visual depiction of both (WS) and direction, highlighting the variability of these factors (Dabbaghiyan et al., 2016). Such a graphical representation aids in comprehending wind patterns across various locations.

Figure 7 illustrates that wind measurement station data in the region show varied speeds, with mean values ranging from North (N) to North-North-East (NNE). The predominant directions differ from one station to another, with NNE (15.21%) dominating at station S4, N (15.35%) at station S1, and WNW (12.41%) at station S14. These data highlight the diversity of prevailing winds in the region, which may impact wind potential assessments.

Figure 7.

Diversity of prevailing winds in the region: an analysis of wind speeds and directions.

Graphical representation of (MWS)

The value of plotting the probabilistic Weibull (WS) data and the scale factor on the same histogram graph lies in the visual illustration of the relationship between these two parameters. This representation focuses on (WS) in the range of 5.6 to 6.4 m/s and gives us a better understanding of how the scale factor influences the shape of the Weibull distribution and subsequently affects the probabilistic (WS) distribution.

From the graph above (Figure 8), stations S7 and S8 represent the best locations for the probabilistic Weibull one scale factor speed with values of 6.315–7.124 m/s and 6.388–7.204 m/s, respectively.

Figure 8.

Graphical representation of wind speed and probabilistic wind velocity.

The analysis reveals significant differences in using various algorithms. The E.M.J, E.M.L, and M.M. techniques are utilized in two of these stations, while the M.L.M method is specifically used in a separate station. The G.M and W.M methods are also implemented in nine and seven unique stations, respectively. This variety in calibration techniques highlights the diversity and complexity of the wind data collected at these sites. Concurrently, in the province of Tétouan, as pointed out by Ouahabi et al. (2020), five algorithms (E.M.J, E.M.L, G.M, E.P.F.A, and the Method of Moments) are in use, demonstrating notable effectiveness for all except the G.M method. This diversity of methods proves crucial for optimally adjusting the actual wind data. Figure 9 illustrates our results.

Figure 9.

Number of stations per algorithm.

Monthly study of (WS)

The average (WS) at the year’s 10 stations (S1–S14) shows significant variation from month to month. Analysis of these data shows that the lowest average (WS) is generally around 4.7 m/s (S14), while the highest average (WS) is around 6.8 m/s (S8). Station S8 regularly has the highest average speeds, while station S14 tends to have the lowest average speeds (Figure 10).

Figure 10.

Monthly representation of wind speed.

Daily study of (WS)

(WS) data for the 10 stations S1–S14 over a 24-hour show significant variations throughout the day. Station S1 records the lowest (WS) from 09:00 hour to 10:00 hour, while station S11 records the highest (WS) from 19:00 hour to 20:00 hour. This diurnal variation highlights the impact of local weather conditions and geographical factors on (WS) (Figure 11).

Figure 11.

Diurnal representation of wind speed.

Weibull plot

The Weibull distribution’s fundamental concept is paramount when analyzing (WS) data. This distribution plays an essential role in the statistical modeling of (WS) and is frequently used to describe the wind characteristics of a particular geographical area. A vital aspect of the Weibull distribution is its configuration, governed by the shape (c) and scale (k) parameters. The graph (Figure 12) below shows the actual database and the eight estimated Weibull curves.

Figure 12.

Comparative analysis of the wind BDD histogram using various adjustments to the Weibull distribution.

From the figure above, several locations have identical values for shape factor k and scale factor c, namely (S21; S18), (S1; S14), (S4; S5), and (S3; S9) and are superimposed in the visual geographic representation. The highest values of k and c are found in locations S7 (2,389;7,124) and S8 (2,433;7,204).

The most likely speed and the speed generating the maximum energy

Through the data in Table 5, we gain a significant insight into the (WS) at two key stations, Station 8 (S8) and Station 7 (S7). These measurements are paramount in designing and operating wind turbines and wind farms. The (WS) that generates the maximum energy ( $v_{me}$ ) and the Most Probable Wind Speed ( $v_{mp}$ ) are key parameters determining the viability of using (WE) in each region. They help to inform the precise planning and optimal exploitation of available wind resources. The numerical results show that station 8 (S8) has a $(v_{me})$ of 9.22 m/s and a $(v_{mp})$ of 5.80 m/s, while station 7 (S7) has a ( $v_{me})$ of 9.19 m/s and a $(v_{mp})$ of 5.68 m/s.

Table 5.

Performance analysis of wind speed prediction models for 10 stations.

Station	Algorithm	$R$	$RMSE$	$MAPE (%)$	$k_{e}$	$v_{me}$	$v_{mp}$
S1	G.M	0.98522590	0.00596424	29.81167695	1.85969262	8.94638805	4.64625989
S3	W.M	0.99813907	0.00224082	45.54287501	1.65791215	8.82611949	5.34606183
S4	M.L.M	0.99683009	0.00284031	37.62157463	1.74233102	9.07484134	5.15289444
S5	E.M.L	0.97838308	0.00708096	32.22734904	1.73955977	8.95825713	5.09746488
S7	W.M	0.99034667	0.00477371	37.11451637	1.63216838	9.18952256	5.67729263
S8	W.M	0.99807043	0.00234473	42.45898984	1.60950418	9.21862242	5.79539425
S9	W.M	0.99547531	0.00325953	39.92761178	1.66590780	8.91328193	5.36584981
S10	W.M	0.99188227	0.00435095	42.42139072	1.77111551	8.97535676	4.98577678
S11	G.M	0.99631765	0.00300905	40.31123097	1.84339594	9.51193269	5.00138182
S14	E.M.L	0.99808211	0.00212789	35.53321737	1.85444761	8.78522222	4.58073136

Power density plot

The power density of the wind plays a crucial role in assessing the performance of wind farms, as it quantifies the energy available in the wind at a specific speed and altitude. A higher power density indicates a more incredible amount of potential energy for wind turbines. However, a theoretical limit known as the “Betz limit” states that wind turbines can only capture 59.3% of the total kinetic energy of the wind. Therefore, although power density is essential, it must be considered alongside other elements, such as wind stability and environmental constraints, when planning wind farms, which are not covered in this article.

The Figure 13 above shows the power density (PD) measurements taken at 23 locations. The triangle defined by points S4, S7, and S11, passing through S8, represents the optimum PD positions, with values between 230 and 260 W/m². This geographical region, located at altitudes ranging from 1200 to 1800 m, is highly recommended for the siting of wind farms. However, it should be noted that almost half of the eastern region’s land surface is unsuitable for wind farms. Nevertheless, the possibility of future generations of turbines designed to operate at low (WS) could change this outlook.

Figure 13.

Estimated power density for the Eastern Region.

Choosing wind power

The Capacity Factor ( $CF$ ) is a critical parameter for assessing the wind potential of a location. It gauges the efficiency of converting (WS) into electricity by comparing actual energy output with the theoretical maximum capacity. A high $(CF)$ indicates that the wind farm is operating at optimal efficiency, producing a significant amount of energy. Conversely, a lower $(CF)$ might suggest unfavorable wind conditions or maintenance periods. It is generally recommended to have a ( $CF$ ) above 25% to ensure the success of a project (Daoudi et al., 2022; Idriss et al., 2019). The energy production of a wind farm is directly linked to its ( $CF$ ), meaning that a higher ( $CF$ ) leads to more significant annual electricity generation.

Figure 14 displays the daily variations of $(CF)$ for EWT DW54-500 turbines in the South-Eastern region. Stations S8 and S11 stand out with peak values of 50.18% and 50.90%, respectively, in the evening. In contrast, stations S1, S4, and S14 recorded slightly lower values, ranging between 45.09% and 45.78%. These findings highlight the importance of time management for the optimal use of (WE) in this area. Additionally, the EWT DW 52-500 turbine analyzed by El Khchine and Sriti (2021) shows excellent performance in coastal areas such as Laayoune, Boujdour, Essaouira, Tantan, and Al Houceima, with a $(CF)$ ranging from 31.2% to 41.3%. This suggests that this Dutch brand is ideally suited for these two studies.

Figure 14.

Calculation of the capacity factor using four wind turbines.

Table 6 summarizes the best locations for combining $CF$ (%) and energy production $E_{out} (KWh / y)$ . Station S8 emerges as the most promising site for enhanced electricity production in the Eastern region, with a $CF$ of 36.97% and an energy output of 1614 MWh/year. These results are particularly encouraging when compared to the Tiznit site, where the ( $CF$ ) is 36.91% at 70 meters altitude for the Vestas V82-0.9MW-70m turbine, with an energy output of 3 GWh (Daoudi et al., 2022).

Table 6.

Numerical value of annual output energy (KWh/year) and capacity factor (%) from four wind turbines.

	Aeronautica 54-750	EWT DW52-500	EWT DW54-500	Unison U50
S1
$E_{out} (KWh / y)$	1,614,199	1,501,682	1,619,468	1,563,394
$CF (%)$	20.23	28.76	31.24	19.58
S3
$E_{out} (KWh / y)$	1,418,088	1,334,205	1,446,570	1,376,057
$CF (%)$	21.58	30.46	33.03	20.94
S4
$E_{out} (KWh / y)$	1,499,059	1,411,194	1,526,526	1,448,160
$CF (%)$	22.82	32.22	34.85	22.04
S5
$E_{out} (KWh / y)$	1,432,351	1,345,418	1,456,927	1,387,974
$CF (%)$	21.80	30.72	33.26	21.13
S7
$E_{out} (KWh / y)$	1,588,450	1,478,061	1,594,258	1,539,837
$CF (%)$	24.18	33.75	36.40	23.44
S8
$E_{out} (KWh / y)$	1,614,199	1,614,199	1,614,199	1,614,199
$CF (%)$	24.57	34.28	36.97	23.80
S9
$E_{out} (KWh / y)$	1,424,130	1,338,530	1,450,415	1,381,667
$CF (%)$	21.68	30.56	33.11	21.03
S10
$E_{out} (KWh / y)$	1,413,766	1,321,115	1,428,600	1,373,313
$CF (%)$	21.52	30.16	32.62	20.90
S11
$E_{out} (KWh / y)$	1,583,498	1,445,585	1,550,693	1,543,098
$CF (%)$	24.10	33.00	35.40	23.49
S14
$E_{out} (KWh / y)$	1,302,742	1,214,269	1,314,545	1,270,485
$CF (%)$	19.83	27.72	30.01	19.34

Conclusion

Our comprehensive research into the Oriental region’s (WE) capacity has identified ten critical locations as highly promising, with sites S4, S7, S8, and S11 showing exceptional promise due to their wind power densities ranging from 230 to 260 W/m². These sites demonstrated capacity factors between 30.01% and 36.97%, signifying a solid potential for (WE) exploitation in the area. Applying the Weibull distribution in modeling (WS) was effective and practical, yielding k-shape factors between 2.055 and 2.433 and scale factors in the range of 6.372–7.204 m/s.

These insights are instrumental in formulating strategies for wind farm development in the Oriental region, thereby facilitating a transition to renewable and more sustainable energy practices. The study also opens doors for future collaborations with organizations like the Moroccan Agency for Sustainable Energy (MASEN) and the Ministry of Energy Transition and Sustainable Development. However, it is crucial to consider the limitations of our study, including uncertainties in wind data and methodological challenges. Further investigation, especially in areas like the Bouarfa province and Melilla, coupled with comprehensive financial analysis, is needed to solidify these findings. This methodology reinforces our initial observations and lays the groundwork for more targeted and region-specific studies in renewable energy.

While our study offers substantial insights, it is constrained by certain limitations. The spatial resolution is relatively wide, approximately 70 km or 0.625° in latitude and longitude. Furthermore, while NASA data was an essential resource, access to direct energy production data would enhance the validation of our results. Implementing wind measurement systems and monitoring additional variables, such as atmospheric pressure and temperature at various altitudes and sites, would be beneficial. Future research should incorporate the region’s unique economic and environmental conditions, focusing on climate change impacts and strategic planning for wind farm installations.

In conclusion, guiding the Oriental region toward an energy mix that includes wind, solar, and hydroelectric power is imperative. This strategic direction aligns with the global trend of developing clean, region-specific energy solutions. Therefore, our study opens up promising possibilities for the future of WE in the Oriental region, making a significant contribution to the pursuit of clean and renewable energy sources.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Badr El Kihel

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