2.1 Data

The GFS is a global weather forecasting model (^{NOAA, 2018}), developed and operated by the National Centers for Environmental Prediction (NCEP), which uses the Gridpoint Statistical Interpolation (GSI) as a global analysis scheme (^{Rajagopal et al., 2007}; ^{Prasad et al., 2011}). The GSI is included in the Global Data Assimilation and Forecasting (GDAF) system at National Centre for Medium Range Wea- ther Forecasting (NCMRWF) and the assimilation runs are performed using the six-hour intermittent method (the system has access to a database observed four times a day), where three main interactions are carried out (between predictions and observations) and the analyses are used as initial conditions for subsequent predictions (^{Prasad et al., 2011}; ²⁰¹⁷). The results of the GFS analyses (meteorological term applied to indicate a model result that is not a forecast) were used with horizontal resolution of 0.5 degrees, 64 vertical levels, and six-hour frequency (0, 6, 12 and 18 UTC). The period considered was from 2013 to 2017 for the entire state of MG. From the zonal (UGRD) and meridional (VGRD) components, the intensities (m s^-1) and directions (º) of the wind were obtained every six hours. Daily and monthly averages were also calculated.

To verify how the GFS analyses represent the weather conditions in the state, observations at 10 m from twelve weather stations between 2013 and 2017 were used (Table I). These weather stations belong to the National Institute of Meteorology (INMET) and were chosen according to the mesoregions of the State of MG. These regions were defined, based on economic and social similarities, by the Brazilian Institute of Geography and Statistics (Brazilian Institute of Geography and Statistics - ^{IBGE, 2018}). For comparison, GFS data were extracted from the nearest grid points of the weather stations. Figure 1 shows the location of the stations and terrain elevation through the state. In the south, the altitude is higher, characterized by the Mantiqueira Mountains (Serra da Mantiqueira). In the north the altitude is more heterogeneous, with the Espinhaço Mountains (Serra do Espinhaço) and the São Francisco River Depression, for example (^{CEMIG, 2010}).

Fig 1 Location of MG state in relation to Brazil, spatial distribution of meteorological stations (+) and topography (m) of MG. Different regions within the state are denoted as R1, R2, …R12. 

2.2 Statistical Analyses

The evaluation of the wind speed and direction from GFS results was made through graphs and wind roses. Data obtained by weather stations were also compared with model results (at 10 m). Seasonal, monthly, and diurnal variability analyses of wind speed data were also performed. The diurnal cycle variability is important, as it allows the identification of the time when the wind reaches its highest intensity in a given location; in general, efficient production of wind energy will occur when the highest wind speed is recorded. The average 6-hour and monthly wind profiles from observational data and GFS results were also compared.

The frequency distribution of wind intensity can be represented by the Weibull distribution. This distribution has been adjusted to the GFS analysis and observational data to identify the constancy of wind intensity around an average value. Note that the Weibull distribution depends only on two parameters: the “k” shape and the “c” scale (^{Chandel et al., 2014}; ^{Wais, 2017}). These parameters were obtained through Equations 1 and 2 respectively, where σ is the standard deviation, v̅ is the average velocity and the gamma function (Γ). The parameter “k” is related to the shape of the wind speed distribution (dimensionless), and it is strictly related to the standard deviation of wind speed data while the parameter “c” is directly related to the average wind speed (ms^-1) (Wais, 2017; ^{Katinas et al., 2018}). The parameters of the Weibull distribution are a simple way to compare different datasets.

2.3 Wind Power Density (WPD)

^{Kalmikov (2017)} indicates that seasonal mean power density (WPD) values are more advantageous than wind speed values, especially when comparing locations with asymmetric frequency characteristics, given the sensitivity of WPD to wind variations. WPD (W m^-2) was calculated from the GFS using Equation 3, widely used nowadays. This methodo- logy was also applied by ^{Hennessey Jr. (1977)}, ^{Patel (2006)}, ^{Silva et al. (2016)}, ^{Reboita et al. (2018a)}, and ^{Emeksiz et al. (2019)}, and considers the air density (ρ = 1.225 kg m^-3) and the wind speed (v):

Calculating WPD per unit area (W m^-2) and considering the maximum power coefficient (cp) imposed by the Betz Law. The Betz Limit shows the maximum efficiency can be obtained from a wind turbine is 59.3%, which means the ratio between the input and output of the wind turbine is one third (^{Manwell et al., 2009}; ^{Burton et al., 2011}). Thus, cp = 0.593.

^{Elliotti et al. (1991)} previously used WPD = 0.955 ρv ³ to calculate tables of wind power density classification for winds measured at 10 and 50 m. Table II is a modified version of the one presented in ^{Elliotti et al. (1991)}, comparing original WPD estimates with those calculated from Eqn. 3 and including data at 100 m.

3.1 Wind Spatial Distribution

Wind seasonal averages at 10 and 100 m are shown in Figures 2 and 3, respectively. Wind averages vary over the seasons due to intensification or weakening of atmospheric systems, mainly associated with the South Atlantic Subtropical Anticyclone (SASA), South Atlantic Convergence Zone (SACZ), and Frontal Systems (^{Reboita et al., 2010}; Reboita et al., 2015; Reboita et al., 2019).

Fig 2 Wind seasonal average at 10 m from 2013 to 2017. Intensity (ms^-1) is shaded and vectors indicate wind direction (º). 

GFS indicates that, in general, the wind at 10 m (Fig. 2) has low intensity, not exceeding 2 m s^-1 in the south and 3.5 m s^-1 upstate. However, the wind speed at 100 m (Fig. 3) shows higher values due to surface roughness which tends to decrease with height. The northern portion of the State shows wind speed average at 10 m between 1 and 2.5 m s^-1 during austral summer and autumn; at 100 m, average values between 3.5 and 4.5 m s^-1 were found, respectively. During winter and spring, wind-speed values increase from 2.5 to 3.5 m s^-1 (at 10 m) and from 4 to 6 m s^-1 (at 100 m). A similar pattern is seen throughout the state. The wind speed at 100 m is equal to the minimum threshold for energy generation during winter and spring (dry season), which is 4 m s^-1 (for small electric wind turbines) and wind turbines on a scale of public utility and 6 m s^-1 (wind farms on larger scales), according to ^{Culture Change (2017)} and The Wind Power (2019). The North (R3, see map in Fig. 1) and Jequitinhonha Valley (R4) regions have the highest wind intensities, agreeing with ^{CEMIG (2010)}. Higher wind speed values during winter and spring indicates a possible anti-correlation between wind and precipitation which presents minimum values in these seasons (^{Silva and Reboita, 2013}; Reboita et al., 2015; Reboita et al., 2017; ^{Reis et al. 2018}) and reinforces a positive factor for the expansion of wind power in the state energy matrix. Wind farms would have greater production in months with low operation of the hydroelectric power plants and thus, energy production would be complementary between the two sources.

Fig. 3 Wind speed seasonal averages at 100 m (ms^-1) from 2013 to 2017. Intensity (ms^-1) is shaded and vectors indicate wind direction (º) 

In agreement with ERA-Interim reanalysis data and RegCM4 model results by ^{Reboita et al. (2018a)}, wind density values show significant differences between northern (R3) and southern (R12) regions of MG and higher wind speed values during winter and springtime. However, ERA-Interim data presented a higher contrast between those regions; while the northern region showed wind intensity lower than 6 m s^-1, the southern region presented values lower than 3 m s^-1, matching those of the GFS analysis.

Another important factor is that the average wind speed is less than the maximum limit, favouring eolic energy generation throughout the day and seasons, minimizing possible structural problems. Results in Figure 4 do not differ significantly from those reported by ^{Paula et al. (2017)}: wind speeds varying from 0.8 to 5.5 m s^-1, more intense in winter and in northern MG. It is worth mentioning that ^{Paula et al. (2017)} used only data from meteorological stations, and, in addition, authors performed vertical extrapolation of wind speed data to estimate values at 100m.

Fig. 4 Wind roses determined for the period 2013-2017 in stations: (A) Belo Horizonte, (B) Curvelo and (C) Formiga, representing: (1) observed data, (2) GFS data (10 m) and (3) GFS data (100 m). The legend is in ms^-1. 

The wind direction pattern at 10 m and 100 m is mainly influenced by SASA, which plays an impor- tant role in the climate of South America. Moreover, as reported by ^{Reboita et al. (2019}), the SASA area expands to south and west in climate projections compared to its current climate position. This expansion of SASA may affect weather conditions, modifying the frequency of dry periods, and directly impacting the energy sector in southeastern Brazil. The SASA gains strength in winter and extends to the western Atlantic Ocean, hampering convective movements and cold fronts in southeastern Brazil and, consequently, reducing precipitation rates (^{Reboita et al., 2015}; ^{Reboita et al., 2017}). Therefore, there is a possible complementarity between wind and hydroelectric power plants mainly during the winter (dry season) when hydroelectric power plants operate at low capacity.

3.2 Analysis of predominant wind direction

Wind direction from GFS results at 10 m was compared with observed wind direction data at twelve sites. Wind roses are presented for the predominant wind direction from GFS at 100 m. ^{Emeksiz et al. (2019)} indicate the wind direction analysis can provide information to support the decision of where to install the wind turbines in order to maximize its efficiency. Table III shows that observational data at 10 m from stations presented variable directions. In contrast, the GFS data at both 10 and 100 m, presented predominant northeast-southeast direction, while showing differences in wind speed, and not satisfactorily simulating the observed direction at 10 m.

As an example, Figure 4 shows that Belo Horizonte (A), Curvelo (B) and Formiga (C) stations have a similar predominant wind direction at 10 and 100 m. In contrast, wind direction from GFS are more homogenously distributed. In general, the wind turbines would be better positioned in the NE-SE direction, where they would experience the highest frequency of winds.

Moreover, Figure 4 indicates that wind direction patterns from GFS do not show significant differences between 10 and 100 m. This absence of changes in the wind direction with height over cities (most of the stations analyzed are located in or close to urban centers) suggests little or no influence of urbanization. However, it is well known that urbanization increases energy loss at the surface, affecting both the intensity and the prevailing wind direction. Large urban centers, which expand as population grows, undergo processes that involve changes in land use and occupancy which, in turn, modify surface roughness conditions. GFS is unable to represent terrain conditions adequately well in the interpolation process of wind direction in these regions.

3.2 Wind variability patterns

In terms of seasonal variability, wind speed averages in MG are lower during austral summer and fall, coinciding with higher rainfall rates which guarantee that hydroelectric plants can operate at maximum efficiency. Wind speed averages are higher between July and October (austral winter) reinforcing potential complementarity between higher wind and lower precipitation. Thus, during the dry season, stronger winds can help meet the state’s energy demand. At 100 m, cities as Uberlândia, Montes Claros, and Teófilo Otoni (located in the Triângulo Mineiro (R1), North region (R3), and Mucuri Valley (R5), respectively) presented wind speed averages close to 6 m s^-1. Observations and results from GFS at 10 m show values between 1.5 and 3 m s^-1. The lowest wind speed averages were registered between February and May.

The comparison between observed and GFS profiles showed similar patterns in most sites (Fig. 5). Best results were found for Belo Horizonte, São João del Rei and Varginha (municipalities where the stations are located in areas with few obstacles, in general, with undergrowth or agricultural plantations), while greater differences can be observed in Diamantina, Montes Claros and Juiz de Fora where stations are located in areas with larger obstacles (such as high rocks in the case of Diamantina) or residential areas (in Montes Claros and Juiz de Fora). In general, the GFS model overestimated values at 10 m when compared to the observations, except in Diamantina, Juiz de Fora and São João Del Rei (also shown by the percentage changes).

Fig. 5 Average monthly wind profile (ms^-1) observed at 8 selected sites (at 10 m, blue line) compared with derived GFS values at 10 m (red dots) and at 100 m (green dots). The black line corresponds to the variance of the observed wind at 10m. 

As for diurnal wind speed variability, at 10 m the highest speed was recorded at 12 h and the lowest between 0 h and 6 h, in agreement with the diurnal cycle of the Earth’s surface temperature. At 100 m, the highest speed occurred between 0 h and 6 h (night and dawn) and decreased throughout the day. Observed and GFS profiles show similar patterns at most sites (Fig. 6). The GFS model also overestimated values at 10 m when compared to the observed values, except in Diamantina and Juiz de Fora.

Fig. 6 Diurnal average wind profile (ms^-1) observed at 8 selected sites (at 10 m, blue line) compared with derived GFS values at 10 m (red dots) and at 100 m (green dots). The black line corresponds to the variance of the observed wind at 10m. 

3.4 Weibull Distribution

Statistics are used in wind studies to represent wind variability and evaluate its evolution, with respect to average values and the probability of occurrence of extreme values, and facilitate the comparison between data sets. When the Weibull shape parameter k presents high values, it indicates little variability of the wind speed around an average value, whereas the parameter c indicates the average value of the data. For observations at 10 m at all sites, k values ranged between 1 and 2.16. The values of c presented greater variability, as can be seen in Table IV. According to ^{Patel (2006)}, when k is equal or close to 1 the Weibull distribution approaches an exponential distribution, as in the case of Montes Claros (top-right panel in Fig. 8, blue line), and it indicates that most days registered calm or very weak winds. When k values equal to or close to 2 (Rayleigh distribution), such as in Belo Horizonte, Diamantina, Juiz de Fora and Uberlândia, present standard distributions of wind speeds (found in most places), and in these cases most days have speeds below the average speed.

All observational datasets showed positive asymmetries, where the modal value < median of the values < average speed value (^{Pishgar-Komleh et al., 2015}). Similar calculations with the GFS datasets at 10 m and 100 m, result in values of k between 2 and 3 (Fig. 7 and 8). Also according to ^{Patel (2006)}, distributions with k = 3 (as in Diamantina and Belo Horizonte) are similar to a normal distribution, where the number of strong winds is equal to the number of light winds (symmetric with respect to the mean). The parameter c, in general, was close to 3 ms^-1 (10 m) and 4 ms^-1 (100 m). Analyses carried out by ^{Ramos et al. (2018)} show distribution patterns as positive examples for eolic energy generation, as they detect only minor problems with the change of the wind (winds with less variability).

Fig. 7 Weibull distributions calculated for observed wind speed at 10 m (blue line) at selected 6 sites for the period (2013 - 2017) and GFS values at 10m (red line) and 100m (green line). 

Fig. 8 Same as Figure 7 for the remaining 6 sites. 

Results from observations and GFS show that the frequency of occurrence of extreme events greater than 8 ms^-1 is less than 1%. The analysis show that the winds have acceptable annual values of k but are lower than those found in regions with high wind potential, such as the Brazilian Northeast (with k values equal to or greater than 6) (^{CRESESB, 2001}).

An accurate and reliable assessment of wind resources plays an important role in the effective use of wind energy (^{Shamshirband et al., 2016}). Given the variety of studies carried out that confirm the efficiency of the Weibull distribution (^{Shoaib et al., 2017}; ^{Katinas et al., 2018}; ^{Souza et al., 2019}) in wind studies, it can be concluded that the results presented show that wind intensity data, provide relevant general information on wind variability.

3.5 Wind Power Density (WPD)

Values of WPD depend on the wind turbine model with different power coefficients (cp), as expressed in Eqn. 3. Figure 9 presents the seasonal average of WPD at 100m, considering the air density equal to 1,225 kg m^-3. The left column in Fig. 9 disregards the maximum power conversion estimated by the Betz Law, which shows maximum yield from a wind turbine to be 59.3% (^{Manwell et al., 2009}). WPD results show lowest values during summer and fall, below 70 W m^-2 with higher values in the north and lower values in the south of MG. During winter and spring values are higher, reaching 150 Wm^-2 in the north region. The right column (Fig. 9) shows WPD seasonal average at 100 m, considering the maximum power conversion estimated by the Betz Law, resulting in an approximate 60% reduction compared to the right column. As cp values depend on the wind turbine chosen, such reduction is variable, and it should be taken into account in the calculations as it influences the relationship between wind speed and generated power density.

Fig. 9 WPD (Wm^-2) at 100 m, from 2013 to 2017. Left column: WPD without considering cp. Right column: WPD considering the maximum cp value (59.3%) of the Betz Limit (^{Manwell et al., 2009}). 

WPD results have a high sensitivity to wind speed; therefore, its values are higher when wind speed values are higher. Regions with wind speed above 4.5 ms^-1 at 100 m have higher wind energy generation potential. However, the values are low when compared to results for the Northeast region of Brazil. ^{Ramos et al. (2018)} found sites in the Northeast (Alagoas State) during the dry season with WPD values around 700 W m^-2, and even during the rainy season, 400 Wm^-2. However, it is important to highlight that the Northeast has wind speeds higher than 8 ms^-1, besides high k values. Other regions with high WPD are located south of Bahia (Northeast region) where several wind farms already operate.

In terms of areas in the State of MG with the highest wind potential, the results confirm areas highlighted by ^{ANEEL (2003)} and ^{CEMIG (2010)}, but with lower wind intensity and WPD values. However, it is important to highlight that the study conducted by ^{CEMIG (2010)} used atmospheric modeling at a higher resolution (3.6 km x 3.6 km) than the GFS data. Thus, considering a spatial scale of 50 km adapted in this work, one can classify the wind potential of MG in Class 1 (Table II).