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ScienceDirect
Energy Reports 00 (2020) 000–000

6th International Conference on Advances on Clean Energy Research, ICACER 2021

April 15-17, 2021, Barcelona, Spain

Correlation between the wind speed and the elevation to evaluate

the wind potential in the southern region of Ecuador

Abstract

In this paper, we use the correlation between the average wind speed and the elevation above sea level to present a regression
model for calculating the average wind speed and evaluating the wind potential in the southern region of Ecuador. After
obtaining the regression model, an adjustment factor based on the topographic slope has been included, mainly since the wind
speed could vary largely as it blows across the lower slope regions or intermediate hills of mountains. Once the wind speed was
obtained, both at 10 m and 100 m, the wind power density was calculated, which includes the impact of wind speed and air
density. Finally, the model accuracy was obtained by comparing other free access data sources including actual data from
meteorological stations, using statistical parameters to quantify the error. According to the results obtained, we find that wind
speed has a good correlation with the terrain elevation of the southern region of Ecuador. The simulated wind speed compared to
the actual data has errors between 7.75% and 16.89%, which indicates that the model can predict with > 83% accuracy. In
addition, both the root means square error and the standard deviations have around 1 m/s of error.

© 2020 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of the 6th International Conference on Advances on Clean Energy Research.

Keywords: Wind potential; average wind speed; terrain elevation; regression model; southern region of Ecuador

1. Introduction

For the spatial planning of the site of a potential wind power plant (WPP), the efficient assessment of the wind
potential is important. However, experimental measurements are generally poorly distributed in a given region;
knowing what the wind potential is, based on close observations, is a topic of interest that encompasses many
methodologies and research activities worldwide. In this research, based on the data history of weather stations, the
statistical regression technique has been used to determine how wind speed is affected by the terrain elevation.
 Author name / Energy Reports 00 (2020) 000–000 2

Nomenclature

𝐶𝑝 rotor efficiency, %
ℎ height or elevation above sea level, m
𝐻 height above the ground, m
𝑃𝑚𝑎𝑥 maximum useful power that supplies the turbine, W
𝜌 air density, kg/m3
𝑤𝑎𝑑𝑗 adjusted wind speed, m/s
𝑤𝑎𝑣𝑔 average wind speed, m/s
𝑤𝐻 wind speed at a certain height above the ground, m/s
𝑊𝑃𝐷 wind power density, W/m2
𝑧𝑜 roughness length, m
𝛻ℎ gradient length vector, %

This paper focuses on the southern region of Ecuador (SRE) as Fig. 1 shows. The SRE is located between the
coordinates 03°30´and 05°00´ south latitude and 78° 20’ and 80° 30’ west longitude. This region covers an area of
27,414.69 km2, equivalent to 10.68% of the national territory, distributed in three provinces: El Oro (5,767.69 km 2),
Loja (11,062.73 km2) and Zamora Chinchipe (10,584.27 km 2) [1]. The maximum distance —in a straight line—
from north to south is 225 km and from east to west about 218 km.

Fig. 1. The geographical location of the southern region of Ecuador and political division.
 Author name / Energy Reports 00 (2020) 000–000 3

The southern region of Ecuador has historically been known to have great wind potential; however, it was during
the last decade that wind measurement campaigns have been undertaken which have made it possible to quantify this
potential [2]. Likewise, since 2012, the Ministry of Electricity and Renewable Energy has made available the Wind
Atlas of Ecuador [2], which presents the annual wind conditions for the entire Ecuadorian territory with a resolution
of 200 m × 200 m. One of the main conclusions of this atlas shows the southern region of Ecuador as one of the
areas with the greatest wind potential, and so the Villonaco Wind Power Plant (VWPP) was located there. This plant
has 16.5 MW of installed power and is located in a mountainous terrain complex of Loja Province at approximately
2720 masl with an average annual wind speed of around 10.5 m/s [3].
In parallel to this, several investigations have been carried out to evaluate the wind potential throughout Ecuador.
These investigations have focused on understanding the wind potential in particular areas, carrying out pre-
feasibility analyses, finding possible sites for WPPs, and studying wind energy policies [4–9]. In another study [10],
have been identified places where possible renewable energy generation plants could be located, the Andes
Mountains and the insular region especially in the provinces of Loja, Pichincha and the Galapagos Islands being the
most favourable in order to take advantage of the wind resource.
Based on a systematic review of literature worldwide, several studies have focused on estimating wind potential
in a specific region using data on wind speed from weather stations and its relationship to terrain elevation. For
example, in [11], a wind speed research has been conducted in two mountainous regions (central China and
Switzerland). For both regions, trends in wind speed have important implications for climate change in terms of
coupled processes on the earth's surface and in the atmospheric boundary layer, such as in high-altitude regions
where much of the planet's freshwater is derived. Other studies [12,13] present a statistical approach and neural
network analysis to estimate the spatial distribution of wind potential in a region where observation stations are
sparsely located. Both linear regression analysis and neural network training were used to predict wind speed at sites
where there is a lack of data. The statistical approach of these studies, especially if large amounts of data are
available, can be used for the estimation of wind potential in other regions with poorly distributed wind speed data,
including coastal and mountainous regions. On the other hand, a recent study [14] uses the WRF (Weather Research
and Forecasting) model to obtain the numerical weather forecast. The results of this study show that, using variables
such as terrain elevation, atmospheric pressure, month of the year and temperature, the algorithm is able to produce
more exact wind speed prediction than the original WRF results and other post- processing models.
Other types of studies to obtain the wind potential in a particular region include mesoscale models [15],
Computational Fluid Dynamics (CFD) [16,17], and methods using statistical-based corrections [18] which have been
used to conduct orographic corrections. Nevertheless, these techniques have not been used in this research since the
computational methods are expensive, require specialized software and are difficult to implement. Furthermore, in
territories with characteristics similar to the study area (Colombia and Venezuela), some research has used other
spatial interpolation methods to determine wind speed (𝑤) based on terrain elevation (ℎ), form 𝑤 = 𝑓(ℎ) [19–21].
In our paper, the single most important data sources in the study area are weather stations. Data from 16 weather
stations were used, most of them belonging to the Ecuadorian Institute for Meteorology and Hydrology (INAMHI,
2020). From these, data were obtained for monthly wind speed at 10 meters high, and after a thorough analysis of
homogenization, those stations with a minimum of 20 years of data (the first eight stations showed in Table 1) were
selected. In addition, data from five weather stations belonging to the National University of Loja (UNL) were used
through a research project funded by the National Secretary of Higher Education, Science, Technology, and
Innovation (SENESCYT) from 2011 to 2014. Likewise, wind speed data from 2012 onwards from aeronautical
stations belonging to the General Directorate of Civil Aviation of Ecuador (DGAC) were used [22]. Finally, actual
data from 2014 to 2018 of the Villonaco Wind Power Plant (VWPP) [3] were statistically analysed.
With wind speed data collected from weather stations, we use the correlation between the wind speed average and
the elevation above sea level to present a regression model for calculating the average wind speed and evaluating the
wind potential in the southern region of Ecuador (SRE). Because the wind speed could vary largely as it blows
across the lower slope regions or intermediate hills of mountains [23,24], an adjustment factor based on the
topographic slope has been included. Therefore, the orographic correction has been used to establish the wind speed
based on the interpolated terrain elevations. Subsequently, the results of our model were statistically compared with
other data sources on wind potential in the study area, namely with Global Wind Atlas (GWA) [25], data obtained
from NASA [26] and Wind Atlas of Ecuador [2].
 Author name / Energy Reports 00 (2020) 000–000 4

The organization of this paper is as follows. Section 2 includes the data sources and the methodology used to
calculate the following parameters: wind speed as a function of elevation, vertical wind speed profile and wind
power density. Section 3 shows the results of the model in order to present average wind speeds at both 10 m and
100 m. Similarly, wind power density maps are obtained. Likewise, the parameters used to measure the accuracy
(and therefore the error) of the proposed regression model are presented and discussed in this section. Finally,
Section 4 includes a summary of the most important conclusions.

2. Material and methods

Our research methodology aims to find the correlation between the average wind speed and the elevation above sea
level. After obtaining the regression model, an adjustment factor based on the topographic slope has been included.
Once the wind speed was obtained, both at 10 m and 100 m, the wind power density was calculated, which includes
the effect of wind speed and air density. Finally, the model accuracy was obtained by comparing it with other free-
access data sources including actual data from meteorological stations, using statistical parameters to quantify the
error. Fig. 2 outlines the procedure from the data sources to the accuracy of the model.

Fig. 2. Outline of the methodology used in this research.

2.1. Digital Elevation Model (DEM)

The SRE has a complex topography due to the presence of the Andes Mountains (elevation varies from zero to
approximately 3900 masl) with the alternation of both valleys and mountains and with the consequent variation of
climatic conditions. These terrain variations can be modelled through Digital Elevation Models (DEM). For the
study area, the DEM was obtained from the Shuttle Radar Topography Mission (SRTM) [27,28] and the initial
resolution of elevation model is 3 arc-second (planimetric spacing of 90 m and altimetric precision of 16 m). The
original DEM dataset was re-gridded from the original altitude data resolution using Kriging's spatial interpolation
gridding method to obtain a finer resolution (Fig. 3).
 Author name / Energy Reports 00 (2020) 000–000 5

2.2. Wind data from weather stations

The weather stations are distributed throughout the width and length of the southern region of Ecuador, in both
rural and urban sites as Table 1 shows. Data consist of average annual wind speed, geographical coordinates, and
elevation above sea level. Fig. 3 also shows the location of the stations, superimposed on the DEM.

Table 1. Weather stations locations with the corresponding elevation and average wind speed at 10 m.
Geographical coordinates
Elevation Avg. wind speed (10m)
No. Code Name (decimal degrees WGS 84)
(masl) (m/s)
Lat, Long
1 M033 La Argelia -4.0372, -79.2036 2171 3.80
2 M142 Saraguro -3.6138, -79.2360 2420 6.00
3 M143 Malacatos -4.2177, -79.2732 1493 4.60
4 M146 Cariamanga -4.3349, -79.5566 1958 3.25
5 M148 Celica -4.1064, -79.9536 1999 4.10
6 M149 Gonzanamá -4.2319, -79.4333 2046 4.20
7 M150 Amaluza -4.5862, -79.4327 1750 3.40
8 M151 Zapotillo -4.3841, -80.2386 180 2.90
9 UNL-1 Padmi -3.7436, -78.6148 808 3.24
10 UNL-2 UNL -4.0317, -79.1996 2136 3.63
11 UNL-3 Zapotepamba -4.0456, -79.7742 1003 3.69
12 UNL-4 Chaquino -4.1824, -80.3417 450 3.32
13 UNL-5 Limones -4.3838, -80.3538 180 3.63
14 DGAC-1 Catamayo -3.9967, -79.3697 1230 3.98
15 DGAC-2 Santa Rosa -3.4442, -79.9958 6 2.14
16 VWPP Villonaco -4,0003, -79,2589 2657 7.35

Fig. 3. Digital Elevation Model of SRE and spatial distribution of the weather stations.
 Author name / Energy Reports 00 (2020) 000–000 6

2.3. Wind speed as a function of elevation

Due both to the complex orography of the terrain and the absence of more weather stations, spatial interpolation
has serious limitations. In this paper, the orographic correction has been used to establish the wind speed based on
the interpolated terrain elevations. In this way, from the data in Table 1, and using the Curve Fitting Toolbox and the
Statistics and Machine Learning Toolbox™ from Matlab®, the grade 4 (Eq. 1) polynomial adjustment regression
model was obtained, indicating that the dependent variable (wind speed) is mostly explained by independent
variability (terrain elevation). Along with other data sources obtained for the same geographic locations (Global
Wind Atlas, NASA, and Wind Atlas of Ecuador) Fig. 4 shows both the wind speed and the elevation values of the
weather stations.

Fig. 4. Average wind speed and terrain elevation obtained from weather stations, along with other data sources for the same geographic locations:
Global Wind Atlas, NASA, and Wind Atlas of Ecuador.

Identifying the simplest polynomial model that explains the relationship between variables is equivalent to
identifying the degree of polynomial from which there is no longer a significant improvement in fit. When
comparing two or more regression models, it is known whether the higher polynomial model provides substantial
improvement by studying whether the regression coefficients of the additional predictors are nonzero. The method
used in this work was to identify which polynomial achieves the best model through cross-validation [29]. The
process is to adjust a model for each polynomial grade and to estimate the Mean Square Error (MSE). The best
model is one from which there is no longer a substantial reduction in MSE. In this sense, the MSE obtained by
comparing the grade 4 model with the grade 5 model (Fig. 5), was observed to be greater than 50; on the other hand,
when comparing the grade 5 polynomial with the grade 6 polynomial, it was observed to be approximately zero.
Based on these MSE results, the grade 4 model is the one used. Higher polynomials do not provide significant
improvement and lower polynomials lose a lot of adjusting capacity.
 Author name / Energy Reports 00 (2020) 000–000 7

Fig. 5. Mean Square Error indicates that the best model is a grade 4 polynomial.

As a result, the regression model for calculating the average wind speed 𝑤𝑎𝑣𝑔 is:

𝑤𝑎𝑣𝑔 = −1.04𝑧 4 + 1.127𝑧 3 + 2.836𝑧 2 + 1.677𝑧 + 4.115 (1)

where the 𝑧 variable is as follows:

ℎ − 1644
𝑧= , 0 < ℎ < 4000 (2)
1346

and ℎ is the height or elevation above sea level, measured in metres.

2.4. Adjustment Factor (Topographic slope)

This work has introduced a simple adjustment factor [30] considering the topographic gradient, which is the
maximum inclination of a terrain surface at a specific point. In matrix DEM applications, topographic gradient
estimates are made using operators that are applied over a defined environment of the point to be evaluated,
involving terrain elevation data [31]. Thus, given an elevation function ℎ(𝑥, 𝑦), where x and y denote the horizontal
quantifiers of position (longitude and latitude) the topographic slope at a point is formally defined as the length of
the gradient vector field. Gradient length vector 𝛻ℎ is given by Eq. 3.

𝜕ℎ 2 𝜕ℎ 2
𝛻ℎ(𝑥, 𝑦) = √( ) +( ) (3)
𝜕𝑥 𝜕𝑦

After calculating the topographic gradient, the following rule allows wind speed adjustments to be made for
distinct slopes: if slopes < 30%, wind speed is ¾ of the initially calculated wind speed. Consequently, the adjusted
wind speed is as follows:

3
𝑤 , 𝛻ℎ ≤ 0.3
𝑤𝑎𝑑𝑗 = { 4 𝑎𝑣𝑔 (4)
𝑤𝑎𝑣𝑔 , 0.3 ≤ 𝛻ℎ ≤ 1
 Author name / Energy Reports 00 (2020) 000–000 8

2.5. Vertical wind speed profile

In the atmospheric limit layer, the wind speed tends to increase as it rises and as the earth's surface exerts friction
or delay action on the wind speed. The representation of this wind speed behaviour with height is what is known as
the vertical wind profile that can be modelled using some different methods [32,33]. The equation that has been used
in this work corresponds to the logarithmic law:

𝐻
ln (𝑧 )
𝑜
𝑤𝐻 = 𝑤𝑎𝑑𝑗 (5)
𝐻
ln ( 𝑜 )
𝑧𝑜

where 𝑤𝐻 is the wind speed at a certain height on the ground, and 𝐻, 𝑤𝑎𝑑𝑗 is the wind speed calculated on the Eq. 4
at a height 𝐻𝑜 of 10 m. In addition, a roughness length of 𝑧𝑜 is used which is given in meters (values from 0.0002 to
3.0) and which depends on the type of terrain, the spacing and the height of roughness (water, grass, etc.). These
values can be found in common literature [34,35].

2.6. Wind power density

Wind Power Density (WPD) is the average annual power per square meter of the swept area of a turbine (W/m2),
and it is calculated for different heights above ground level. Calculation of WPD includes the influence of wind
speed and air density [36,37]. Therefore, all wind energy is not able to be harnessed through the turbine, and under
this consideration, the maximum wind power density (𝑊𝑃𝐷𝑚𝑎𝑥 ) that is delivered by a wind-energy conversion
system is expressed by the following equation:

𝑃𝑚𝑎𝑥 1
𝑊𝑃𝐷𝑚𝑎𝑥 = = 𝜌𝑤𝐻 3 𝐶𝑝 (6)
𝐴 2

𝑃𝑚𝑎𝑥 is the maximum useful power that supplies the machine, which is driven by the wind, 𝜌 is the air density
expressed in kg/m3, and 𝐶𝑝 is the rotor efficiency.
The theoretical maximum rotor efficiency is 0.59 [36]. This factor is known as Betz Efficiency or Betz Law
[37,38]. In practical designs, the maximum achievable rotor efficiency ranges between 0.4 and 0.5 for modern high-
speed two-blade turbines and between 0.2 and 0.4 for slow-speed turbines with more blades. In this work, 𝐶𝑝 = 0.5
was considered as the practical maximum rotor efficiency; therefore, the maximum wind power density output of
the wind turbine is rewritten as the simple expression:

1
𝑊𝑃𝐷𝑚𝑎𝑥 = 𝜌𝑤 3 (7)
4 𝐻

Finally, for heights other than sea level, density can be calculated by the equation:

𝜌 = 𝜌𝑜 − 1.194 × 10−4 ℎ (8)

where 𝜌𝑜 is the air density at sea level. The Eq. 8 is valid up to a height above sea level of 6000 m [36].

3. Results and discussion

Using DEM, the topographic gradient (Fig. 6), as well as all maps presented in this work were programmed and
presented with the surface and contour mapping software SURFER® 3D.
 Author name / Energy Reports 00 (2020) 000–000 9

3.1. Topographic gradient

Wind Power Density (WPD) is the average annual power per square meter of the swept area of a turbine (W/m 2),
and it is calculated for different heights above ground level. Calculation of WPD includes the influence of wind
speed and air density (Patel, 2006; Villanueva and Feijóo, 2010). Therefore, all wind energy is not able to be
harnessed through the turbine, and under this consideration, the maximum wind power density (𝑊𝑃𝐷𝑚𝑎𝑥 ) that is
delivered by a wind-energy conversion system is expressed by the following equation:

Fig. 6. Topographic Map Slope (Gradient) of the SRE.

Fig. 7. (a) Average wind speed at 10 m; (b) average wind speed at 100 m.
 Author name / Energy Reports 00 (2020) 000–000 10

3.2. Average wind speed in the SRE

From here, the programming of equations 4 and 5 results in wind speed maps for the southern region of Ecuador
(Fig. 7) at heights of 10 m and 100 m respectively.

3.3. Wind power density in the SRE

Similarly, when applying the Eq. 7, the wind power density maps are obtained (Fig. 8), again, for heights of both
10 m and 100 m.

Fig. 8. (a) Wind power density of SRE at 10 m; (b) wind power density of SRE at 100 m.

To characterize wind potential in the southern region of Ecuador, this work has used the wind power
classification scheme shown in Table 2. This scheme was developed as part of the U.S. Department of Energy's
Federal Wind Energy Program and was presented in the Wind Energy Resource Atlas of the United States [39,40].

Table 2. Classes of wind power density at 10 m and 100 m.

Wind Wind power Wind speed Wind power Wind speed1
power Resource class density at 10 m at 10 m density at 100 m at 100 m
class (W/m2) (m/s) (W/m2) (m/s)
1 Not suitable < 100 < 4.4 <270 < 6.14
2 Marginal 100 - 150 4.4 – 5.1 270 - 405 6.14 – 7.12
3 Moderate 150 - 200 5.1 – 5.6 405 - 538 7.12 – 7.83
4 Good 200 - 250 5.6 – 6.0 538 - 674 7.83 – 8.38
5 Excellent 250 - 300 6.0 – 6.4 674 - 807 8.38 – 8.94
6 Outstanding 300 - 400 6.4 – 7.0 807 - 1000 8.94 – 9.78
7 Superb > 400 > 7.0 > 1000 > 9.78

1
Vertical extrapolation of wind speed is based on Eq.5.
 Author name / Energy Reports 00 (2020) 000–000 11

3.4. Accuracy of the model

The parameters used to measure the accuracy (and therefore the error) of the proposed regression model are
presented in this section. In this regard, several authors have proposed different statistical parameters to quantify the
error [41-43]. In this work, because no individual statistical parameter is fully satisfactory, four statistical
formulations have been chosen as follows: i) Mean Absolute Percent Error (MAPE) is the most common measure of
forecast error. MAPE is the average absolute per cent error for each time simulated data minus current divided by
current. With zero or near-zero values, MAPE can give a distorted picture of the error. The error on a near-zero item
can be infinitely high, distorting the overall error rate when it is averaged in. For forecasts of items that are near or at
zero volume, Symmetric Mean Absolute Percent Error (SMAPE) is a better measure. ii) SMAPE is an alternative to
MAPE when there is zero or near-zero demand for data. SMAPE self-limits to an error rate of 200%. However, a
percentage error between 0% and 100% is much easier to compare with other statistical parameters. Thus, SMAPE
can be defined as the simulated values minus current divided by the sum of simulated values and current. iii) Root
Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors), so it is expressed in the
same measurement unit. Residuals are a measure of how far points are from the simulated data. In other words, it
describes how concentrated the data is around the line of best fit. RMSE is commonly used in forecasting and
regression analysis to verify experimental results. Finally, iv) Standard deviation (σ) is a measure of the dispersion
of a set of data from its mean and is also expressed in the same measurement unit. It is calculated as the square root
of variance by determining the variation between each data point relative to the mean. If the data points are further
from the mean, there is a higher deviation from the data set.
Therefore, errors (Table 3) have been calculated, comparing the results of the model (Fig. 7) with the average
wind speed data from different sources: Weather Stations, Global Wind Atlas, NASA, and Wind Atlas of Ecuador.

Table 3. Error calculation of our model compared to other wind speed source data.
MAPE SMAPE RMSE 𝜎
Data source
(%) (%) (m/s) (m/s)
Weather stations 16.89% 7.75% 0.80 0.48
Global wind atlas 32.01% 13.54% 1.41 0.98
NASA 32.29% 13.65% 1.43 1.01
Wind atlas of Ecuador 19.22% 9.45% 0.88 0.44

On the one hand, the simulated wind speed compared to the actual data has errors between 7.75% and 16.89%,
which indicates that the model can predict with > 83% accuracy; this is very useful when there is a low density of
weather stations. Similarly, both the RMSE and the standard deviation have less than 1 m/s, which is a small value
compared to the wind speed levels handled. On the other hand, comparing the results of the model with other data
sources (GWA, NASA, WAoE), errors range from 9.45% to 33%. This is to be expected, mainly because our model
was made using only actual data from weather stations. However, considering that the model is very simple, easy to
implement and did not required complex models (CDF or mesoscale), 66% accuracy is an acceptable value for
authors.
Another way to compare the proposed model with other data sources is by calculating its coefficient of
determination (R2), as shown in Fig. 9.
 Author name / Energy Reports 00 (2020) 000–000 12

Fig. 9. Coefficient of determination by comparing modelled average wind speed with (a) weather stations data, (b) Global Wind Atlas, (c) re-
analysis data obtained from NASA, and (d) Wind Atlas of Ecuador.

As observed in Fig. 9, the largest adjustment is when R squared is ≈ 0.7. This means that the model explains by
70% the wind speed depending on the terrain elevation. Similarly, comparing the model with both the Global Wind
Atlas and the Wind Atlas of Ecuador, it is observed that they have coefficients of determination between 46% and
65% respectively, mainly because they use mesoscale models and not point data from weather stations.
One of the most important applications of our model is the independence of spatial terrain resolution. For
example, for the construction of the Wind Atlas of Ecuador, the Mesoscale Atmospheric Simulation System
(MASS) was used [44]; however, the MASS has been implemented with a resolution of 2.5 km. Similarly, the
Global Wind Atlas uses a downscaling process. Here, the data are located on a grid with a spacing of approximately
30 km. This data is used to force the Weather Research and Forecasting mesoscale model [45] using a grid spacing
of 3 km. On the other hand, wind-speed data from NASA's data-access-viewer was obtained through model-based
analyses of multiple datasets using a fixed assimilation system like the Global Modeling and Assimilation Office
(GMAO) mission. The GMAO's mission to provide modelling support for NASA's satellite observations
encompasses the need to examine the impacts of different observation types in weather and climate prediction.
Because of this, and since it does not use mesoscale models or weather stations data, the wind- speed values are
relatively similar for the entire study area, which explains the low level of correlation with the proposed model.
On the other hand, the spatial resolution independence allows for the analysis of the wind potential in different
locations, provided that data on the elevation of the terrain is available. For example, Fig. 10 shows the potential of
the wind resource for the Villonaco Wind Power Plant site [3] using the model proposed in the present work.
 Author name / Energy Reports 00 (2020) 000–000 13

Fig. 10. Wind resource of Villonaco site in which Villonaco Wind Power Plant is located.

At the Villonaco site, other studies about wind potential have been carried out using different methods of analysis
[46,47], in which the annual average wind speed of all wind turbines was compared with the average wind speed
predicted by a CFD tool based on a nonlinear flow model, as Fig. 11 shows.

Fig. 11. (a) Orographic map of the VWPP with wind turbine positions in UTM (Universal Transverse Mercator) coordinates; and (b) annual
average wind speed at 100 m. Source: [46,47].

In addition, actual data (every 10 minutes) have been obtained in this particular site during five years of
observations (from 2014 to 2018). These data have also been used to compare model error, as shown in Table 4.
 Author name / Energy Reports 00 (2020) 000–000 14

Table 4. Error calculation of our model compared to other wind speed source data for the Villonaco site.
MAPE SMAPE RMSE σ
Data source
(%) (%) (m/s) (m/s)
CFD analysis 17.32% 7.87% 1.57 0.48
Actual data (2014-2018) 5.52% 2.72% 0.66 0.33

By making a comparison with the data predicted by the CFD tool and with the actual data, our model has
obtained errors ≈3% (for actual data) up ≈17% for CFD-modeled data. Likewise, in both cases it does not exceed
0.5 m/s of standard deviation, indicating that on average, the wind speed calculated with our model for the Villonaco
site does not exceed 0.5 m/s with the actual wind speed measured. It should be noted that the actual data for the
wind turbines correspond to a height of 67 m (wind turbine hub height). This further justifies the results obtained in
Table 4.

4. Conclusions

The following conclusions have been drawn from the analysis done on the correlation between average wind
speed and elevation in order to evaluate the wind potential in the southern region of Ecuador:
Based on a systematic literature review, it can be concluded that the analysis of wind potential in particular
regions follows several methodologies, from simple statistical analysis to the use of powerful simulation and
forecasting tools. In this study, a regression model is presented using the correlation between the average wind
speed and the terrain elevation, including an adjustment factor based on the topographic slope, for calculating the
average wind speed and evaluating the wind potential in the southern region of Ecuador.
The results of our model have been compared with those of other sources that analyse the wind potential in the
area of study. These include actual data from 16 weather stations, data from the Wind Global Atlas, data from the
NASA website, and data from the Wind Atlas of Ecuador. The simulated wind speed compared to the actual data
has errors between 7.75% and 16.89%. Similarly, the data obtained from the model compared to the other sources of
information ranges between 9.45% and 32.29%. In addition, in all cases, both the root means square error and the
standard deviations have around 1 m/s of error.
One of the most important applications of our model is the independence of spatial terrain resolution. This means
that knowing the terrain elevation map within the SRE makes it possible to calculate the wind speed and wind power
density. The latter was validated with experimental data from the Villonaco zone, with errors less than 5.52%.

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