Identification of optimal wind, solar and hybrid wind-solar farming sites using fuzzy logic modelling

Energy 188 (2019) 116056

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Identification of optimal wind, solar and hybrid wind-solar farming sites using fuzzy logic modelling A.Z. Dhunny a, *, J.R.S. Doorga a, Z. Allam b, M.R. Lollchund a, R. Boojhawon c a

Department of Physics, Faculty of Science, University of Mauritius, Mauritius Curtin University Sustainability Policy Institute (CUSP), Curtin University, Australia c Department of Mathematics, Faculty of Science, University of Mauritius, Mauritius b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 March 2019 Received in revised form 19 August 2019 Accepted 1 September 2019 Available online 3 September 2019

In this paper, an analytical framework is developed using fuzzy logic to evaluate optimal sites for wind, solar and hybrid wind-solar farms; using criterial components for energy optimization through climatological, topographic and human factors. The model is applied through a case study to the island of Mauritius which bears a highly complex topography. Through this computation, fuzzy constraints including wind and solar power, site elevation, settlement areas, and proximity to grid lines are all fitted to different fuzzy membership sets and the individual satisfaction degrees of each were calculated and aggregated into overall satisfaction degrees. Decision maps of highly suitable regions for hybrid windsolar farming were then highlighted revealing two potential sites on the island for hybrid wind-solar farming; revealing a total generation potential of energy per year of 161.58 GWh at Le Morne and 281.28 GWh at La Laura-Malenga. The findings of this study aim to guide energy and urban planners to better identify optimum sites for wind, solar and hybrid wind-solar farm construction whilst making optimal use of land resources to achieve both sustainable dimensions and energy economic resilience. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Optimization Hybrid wind-solar farm Fuzzy logic system Decision maps

1. Introduction The world is witnessing a demographic boom leading to increasing consumption patterns and stressing on natural resources. Environmental issues have been noted as a result of this and the latest report of the Intergovernmental Panel for Climate Change (IPCC) [1] notes alarming consequences, showcasing the vital importance to explore alternative and renewable energy sources over fossil fuels [2], and which boasts less environmental concerns [3,4]. Interestingly, out of the available renewable energy sources, wind and solar energy stand as the most popular, where wind farming has acquired a worldwide wind power capacity exceeding 540 GW in 2017 [5] with the worldwide offshore wind power at 18.8 GW [6]. Similarly, solar power has increased significantly over the past five years, with capacity quadrupling to reach a total generating capacity of nearly 400 GW in 2017 [5]. The rapidly growing wind and solar energy market has led to many new challenges, with a notable one being land use management. Wind turbines are usually installed in a cluster in the farm so

* Corresponding author. E-mail address: [email protected] (A.Z. Dhunny). https://doi.org/10.1016/j.energy.2019.116056 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

as to reduce operation and maintenance costs [7e10]. Therefore, the optimization of such installations is primordial to ensure sound economic throughputs. Solar panels on the other hand face the major constraint that they need appropriate land slopes so that they do not face the shading effects that one row casts onto another. On this front, the thematic of land use for solar and wind energy, however, persists especially for Small Island Developing States (SIDS) where land is very scarce [7]. One solution lies in maximizing land use to encourage a symbiotic model of energy co-generation; through a hybrid wind-solar farm layout, which can work perfectly as solar farms occupy ground level surface whilst wind turbines are mounted on a vertical axis. Using the same site then allows for the opportunity to capitalize on optimal energy yields from both energy sources on a combined smaller amount of land, rendering it more appealing for developers. A review of literature reveals that the optimization of hybrid wind-solar farms has been implemented on various platforms using distinct techniques [11]. Borowy et al. [12] used a graphical construction technique to size the combination of a battery bank and photovoltaic array in the US. Tina et al. [13] employed a probabilistic approach for modelling the long-term performance assessment for the island of Stromboli in Italy. Yang et al. [14] used a

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genetic algorithm method to determine the optimum design and techno-economic analysis in Hong Kong. The use of GIS in this approach provides interesting findings as showcased by Jahangiri et al. [15] for case studies in the Middle-East, and by Ayodele et al. [16] for the case of Nigeria, where a multi-criteria GIS model has been developed using Interval Type-2 Fuzzy AHP taking into consideration economic, social and environmental factors. Going further, Wu et al. [17] used a fuzzy-MADM approach to determine optimal location sites of offshore wind farms in the waterways of China and a GIS MCDM method was employed in South Korea to determine the optimum on-shore wind farm site locations [18] and in the Kingdom of Saudi Arabia [19]. A further review of literature showcases that Nazari et al. [20] used a TOPSIS approach to determine the best locations for solar PV deployment in Iran. A fuzzy logic model combined with weighted linear combination technique was used to determine optimum sites for the placement of solar farms in the arid and semi-arid region of Isfahan-Iran [21]. A GIS based Boolean-Fuzzy logic method was employed by Yousefi et al. [22] to find most appropriate regions for the construction of solar power plants in the Markazi Province of Iran. Another GIS technique, coupled with AHP method was used to site large scale PV locations in Eastern Morocco [23] and a decision support model was developed to locate solar power plant sites in Thailand [11] and a risk management of wind farm micro-siting has been carried out in Taiwan using an enhanced genetic algorithm with simulation optimization [24]. Against this backdrop, there is a clear gap in literature as to the combination of both Solar and Wind energy for hybrid models to achieve optimal land use. As such, this paper attempts to address this through the use of a fuzzy logic optimization system computing various components such as slope of the land, settlement regions and proximity to grid transmission lines in order to formulate a robust model on the MATLAB™ platform. Arguments are put forth showcasing advantages offered by the fuzzy logic modelling approach where it has been noted as being continuous and therefore allowing the individual parameters to take various truth degrees from being absolutely true (1) to being definitely false (0). Consequently, the novelty of this paper is highlighted by the availability of identifying sites with a potential for generating energy from a combination of both Wind and Solar through the application of the fuzzy logic approach to the renewable energy sector with the aim to develop an optimization model for wind, solar and hybrid wind-solar farms. This technique can provide investors with a better economic yield through a more stable and resilient grid. While numerous other techniques exist to increase efficiency and yield, the authors explore the applicability of the fuzzy logic approach in complex terrains through the case study of the Small Island Developing States (SIDS) of Mauritius and demonstrate its viability. The organization of the paper is as follows: section 2 describes the study area and gives a background on the share of renewable energy, especially wind and solar, in electricity generation, section 3 elaborates on the methodological framework of the technique employed; section 4 presents the results and discussions; section 5 gives the conclusive remarks pertaining to the construction of the hybrid wind solar farm in Mauritius or SIDS in general. 2. The study area Mauritius, an island located in the tropics with latitude 20
170 South and longitude 57
500 East (shown in Fig. 1), has a total land area of 2040 km2 and an estimated population of about 1.27 million. The population density of the country is about 630 people per square kilometer, which ranks it 19th in the world [25];

Fig. 1. Study area (Mauritius) located in the South-West Indian Ocean (Illustration by Authors).

however, the density of urban areas is much higher [26]. Exacerbated land degradation stemming from climate change coupled with an increasing land use for urban development and construction are putting high pressures on the limited land availability in Mauritius [27]. Consequently, sustainable land management practices are being implemented by policy-makers. This is however deemed as a challenge as issues of ownership and custodian rights come in place. Sandwiched between increasing concerns of climate change [1] and a rapidly increasing demographic [28], the island - a Small Island Developing States (SIDS), faces land management concerns due to its size and rapid urban growth, and more cautious choices have to be made in respect to renewable energy technologies that do not occupy vast spatial extents. It is therefore faced with a dilemma of investment in renewable energy technologies at a cost in both economics and land. In this respect, wind energy production is seen to occupy less land extents as opposed to other renewable energy solutions. Along this line, it is noted that a share of 0.5% of the electricity generation of the island emanates from a wind farm situated at Plaines des Roches (in the East of the island), having a total capacity of 9.35 MW and comprising of 11 turbines, with provisions made to accommodate 10 more turbines which will increase its yearly generation capacity to 14.5 GWh [29]. Future plans to harness wind energy include the commissioning of 20 MW wind farms at regular intervals of 3 years as from 2017; emerging from a general consensus to the energy strategy of the

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Table 1 Techniques employed in literature, their merits and gaps. Authors

Method

Merits

Rezaei et al. [34] Jun et al. [35] Yun-na et al. [36] Jahangiri et al. [15] Aktas et al. [37]

Fuzzy TOPSIS combined with Weibull distribution function and AngstromPrescott equation ELECTRE-II

Sensitivity analysis performed using MCDM methods to Final rankings can swap as new alternatives are integrated verify validity of results. in the model.

Ideal Matter-Element Model

Boolean model and GIS

Hybrid hesitant fuzzy decision-making approach

Demerits/Gaps

The process is intelligible and can bear the responsibility for decision-making in the evaluation process. This method is effective at distinguishing which quality level the hybrid wind-solar power stations sites should belong to. Boolean logic deals with complex systems through simple logical relationships rather than assigning precise numerical values. Using fuzzy expressions make it simpler for decision makers to give linguistic and uncertain definitions.

Attribution of weights may be biased based on the judgement of a group of decision makers. Difficulty arises when Matter-Elements are in the same level. Additionally, this method also seeks expert opinion for model building. The major limitation of Boolean modelling is that it gives only definite black and white results, with no in-between possibilities. Considering only quantitative factors may result in taking some qualitative factors out of consideration.

Table 2 Strengths and weaknesses of the software used in literature. Authors

Software Strengths

Weaknesses

Aydin et al. [38] Vasileiou et al. [39] Azizi et al. [40] Zucca et al. [41]

ArcGIS

The license fee for running the software is relatively expensive.

Displays high resolution and refined spatial mappings with an assorted variations of color palette. QGIS Besides being open-source, QGIS is a cross-platform software and is adaptable on Linux, Mac and Windows. MATLAB Enables complex processing to be performed on spatial and temporal scales. ILWIS Compact package with a range of vector and raster-based GIS functions.

island [30]. In addition to a number of small and medium scale distributed generation systems, Mauritius is equipped with a 15.2 MW solar farm situated at Bambous (in the West of the island). In 2015 and 2016, the Central Electricity Board (CEB), which is the main organization responsible for the generation, transmission and distribution of electricity on the island, issued tenders for a total of 62 MW for the construction of additional solar farms to be commissioned in 2018 and 2019 [31]. As renewable energy furthers its integration in the Mauritian energy landscape, we note that its integration is treated in isolation and hybrid systems are not considered, mainly perhaps due to the lack of studies on this context; to which, this paper responds. 3. Methodology For the exercise of land identification in Mauritius for a hybrid wind-solar farming, a framework is prepared based on human,

The quality of the cartographic output is weak as compared to ArcGIS. The cartographic maps produced by MATLAB is of low quality as compared to the other GIS software. Additionally, the license fee is quite costly. This software often has bugs and instabilities that limit its use.

climatological and topographic factors. For example, human factors are based on the proximity of the settlement areas and grid transmission lines to the hybrid wind and solar farm, public recreational area and agricultural land; climatological factors are based on the wind and solar resource assessments; and the topographic factors depend on the appropriate slope angle of the terrain under investigation. Building from previous methodological structures on similar works, investigations revealed that in a previous work by Dhunny et al. [32], a Geographic Information System (GIS) was used by the authors set forth to find the best wind farm location in Mauritius. Wind data at 100 m were filtered such that wind speed less than 7.0 m/s were rejected. A slope map was designed which eliminated all regions which has slope greater than 10
, as per the IEC constraint and a Settlement area map was overlaid over the wind and slope maps to display all the allowable regions [32]. The best wind farm location was then found visually. In another work

Fig. 2. (a) Wind speed map at 60 m.a.g.l [43], (b) Wind speed map at 100 m.a.g.l [43] (c) Yearly mean daily global solar irradiation map [44].

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performed by Doorga et al. [33], to determine the optimum locations for the placement of solar farms on the island, a multi-criteria GIS technique was adopted and coupled with the analytical hierarchy process to combine climatological factors comprising of solar radiation, air temperature, sunshine duration and relative humidity; topographic factors comprising of elevation, slope and aspect; and location factor comprising of proximity to grid and road networks. This combination resulted in a suitability index using an algebraic mathematical combinatorial technique which was thereafter overlain on a constraint map of the island to reveal favorable and unfavorable locations for the construction of solar farms. This present work adopts a combination of both the above methodologies by using a more comprehensive and logical approach for optimized placement of hybrid wind and solar farms. The perceived primary benefit of a hybrid wind-solar farm is that the weakness of one renewable energy technology may be compensated by the strength of the other. Wind power has the weakness of variability in electricity generation attributed to the heterogeneity of wind conditions on temporal scales and the heterogeneity associated with cloud conditions is regarded as a major limitation in solar harnessing. However, if the two systems are combined, the opportunities for energy generation are amplified at any given time and condition. Table 1 shows some techniques employed in literature and their corresponding merits and demerits. The strengths and weaknesses displayed by various software used in spatial variable analysis are displayed in Table 2.

the highly complex terrain of Mauritius using a second order upwind scheme along with the k-epsilon RNG turbulence model [32]. The resulting wind maps are displayed in Fig. 2(a)-(b). 3.2. Solar resource assessment The solar data employed in this study comprise of long-term yearly mean daily global solar irradiation values recorded by the Mauritius Meteorological Services (MMS) over the years 1961e1990 at 15 spatially well distributed stations over the island. The method of Inverse Distance Weighting (IDW) interpolation technique was used in order to provide a continuously varying parameter over the island of Mauritius and was fully validated through a solar model analyzed by Doorga et al. [42]. The resulting solar map is displayed in Fig. 2(c). 3.3. Topography of the study area The topographic map of Mauritius is shown (Fig. 3(a)). It depicts the height around the island as well as the settlement areas. The slope map was created by using DEM data in GRASS GIS 7.2.1 software environment. The DEM data has a resolution of 15 m. Slope analysis is an important factor when considering wind farming locations, because the steeper the slope, the higher the cost of the wind farm will be. Additionally, steep slopes may cause unwanted shading effects of one row of solar panels onto another. In this study, slopes which are greater than 15
are eliminated and in Fig. 3(b), it can be observed that most of the island is flat except for mountainous regions.

3.1. Wind resource assessment 3.4. Fuzzy logic system modelling The wind data used for this work consist of long term yearly mean hourly wind speed data which was recorded by the Mauritius Meteorological Services (MMS) over the years of 1942e2016 at 7 stations all over the island. The Computer Fluid Dynamics (CFD) software WindSim 6.0 has been used to model the wind flow over

There is numerous research on the potential benefits of Artificial intelligence to the engineering field [16,45]. Fuzzy logic has been a common tool used by scientist to dwell into the interpretation of data for precise outputs [17,46]. The technique basically aims at

Fig. 3. Generated map of the island of Mauritius with (a) settlement and (b) slope constraints under consideration.

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reproducing the reasoning used by human experts in a certain field. This is done by using a model based on a person's experience rather than merely mathematical equations. The main strength of fuzzy logic is that it uses human terms and descriptions rather than abstract numbers in making the decision. Most fuzzy sets are used to represent the criteria or objectives which do not have crisp (precise) boundaries usually due to non-availability of information about the criteria or objectives. For example, for a crisp set A, an element x in the universe is either a member of the set A or may not be a member. Fig. 4(a) illustrates crisp binary sets of ‘tall’ and ‘not tall’ people [45]. On the other hand, fuzzy algorithms allow the possibility to widen the search to the set of real numbers. The fuzzy set approach to the set of tall people provides a much better representation of the tallness of a person. The set shown in Fig. 4(b) is defined by a continuously inclining function. If, for example, people taller than or equal to 180 cm are considered to be tall, then this set membership can be represented graphically via Fig. 4(a). So it is either you are tall or you are not tall. This works perfectly for binary operations and mathematics, but in fact this does not reflect well for describing the real world. This particular membership therefore does not make a difference between somebody who is 180 cm and

5

175 cm, they both are simply considered as tall, which is an erroneous analysis [45]. The Fuzzy logic membership, gives a more accurate representation of the tallness of people. The range is defined in Fig. 4(b). It defines the fuzziness for the possible values underneath of the horizontal axis, whereas the vertical axis on a scale of 0e1 arrogates the membership value of the height in the fuzzy sets. Therefore, if consideration is made for a person having a membership of 0.3, it will mean that the person is not very tall but the person who has a membership of 0.95 is definitely tall.

3.4.1. Fuzzy logic theory Contrary to the traditional set theory which is based on bivalent logic where a value or parameter is a member of a set or not, fuzzy logic permits a value or parameter to be a member of more than one sets whilst introducing the concept of partial membership [47]. A scale of 0 (no membership) to 1 (complete membership) is employed to define the degree of membership in a set. The structure of the fuzzy logic system comprises of three main steps which include fuzzification, fuzzy inference and defuzzification. During the fuzzification stage, the input variables are decomposed into distinct fuzzy sets. Afterwards, fuzzy inference process takes place

Fig. 4. Hypothetical representation of sets for ‘tall’ and ‘not tall’ people [45].

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Fig. 5. Fuzzy input/output combination.

whereby a set of fuzzy if-then-else rules are adopted to generate a fuzzy output. Finally, defuzzification occurs whereby the outputs from all the individual fuzzy rules are weighted and averaged into a single output decision [47]. A fuzzy member is a function, e.g u: ℝ/[0,1], which satisfies the following conditions as stated by Ref. [48]:  u is an upper semi-continuous function on ℝ,  u(x) ¼ 0 outside some interval [a,d],  for a, b, c, d are elements of ℝ with ab  c  d, i. u(x) is a monotonic increasing function on [a,b], ii. u(x) is a monotonic decreasing function on [c,d], iii u(x) ¼ 1, c x 2 [b,c]. Following those conditions, if uL:[a,b] /[0,1] and uR:[c,d] /[0,1] be the left and right membership functions of the fuzzy number u, respectively, then the membership function of u is represented in equation (1) as:

uðxÞ ¼

8 > > > > > > ðx  x0 þ sÞ=s; x0  s  x  x0 ; > > > > > > < 1; x0  x  y0 ;

(2)

> ðy0  x þ bÞ=b; y0  x  y0 þ b; > > > > > > > 0; elsewhere: > > > > :

while the two defuzzifiers x0, y0 and left fuzziness s > 0 and right fuzziness b > 0: Note that when x0 ¼ y0, then u is referred to as a triangular fuzzy number and is represented as u¼(x0, s, b). In this paper, the Mamdani fuzzy interference method was used [50] as it is closest to the human understanding as we have a large number of rules in decision making (The Fuzzy input/output combination is shown in Fig. 5) and is given in equation (3):

    cr2R : if ∧1in xi 2Ari then∧1jm yj 2 Brj

(3)

where xi is the input variable, yj is the output variable, Ari is the input fuzzy set of input variable i and rule r, Brj is the output fuzzy set of output variable j and rule r, and n is the number of input variables.

8 > > u ðxÞ; a  x  b; > > < L 1; b  x  c; uðxÞ ¼ > > uR ðxÞ; c  x  d > > : 0; elsewhere:

Table 3 Truth table for a bivalent set.

(1)

Fuzzy number u, is said to be positive or negative which are denoted by the fact that u is greater than 0 or less than 0, if its membership functions u(x) is 0 for all x < 0 or x > 0. It should be noted that the set of all fuzzy numbers is a convex cone which is embedded isomorphically and isometrically into a Banach space [49]. When u (r) ¼ u(r), the fuzzy number is simply referred to as a crisp number. The trapezoidal fuzzy number u¼(x0, y0, s, b), is a fuzzy set where the membership function is given by equation (2):

x

y

x AND y

x OR y

NOT x

0 0 1 1

0 1 0 1

0 0 0 1

0 1 1 1

1 1 0 0

Table 4 Truth table for fuzzy logic in generalized form. x AND y x OR y NOT x

Min(x,y) Max(x,y) 1-x

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3.4.2. Representation of the different factors in fuzzy sets In fuzzy logic, there are several operators (AND, OR, NOT) which are employed as per the prerequisite of the problem. But for bivalent logic the Boolean operators behave differently as compared to the fuzzy logic. Tables 3 and 4 show the difference between the operators for bivalent sets and for fuzzy logic. In this case scenario, we are developing potential location of wind farms. The slope of the terrain, the settlement areas, and proximity to grid lines and wind conditions are all considered and thence, those parameters will be represented as fuzzy sets to evaluate the best placement of the wind farm for the case study. Therefore, the operator AND is employed, as it helps to combine many criteria together [49]. As fuzzy sets are used to represent the objectives which do not have crisp boundaries, the settlement area for this case is fixed to include precise sets which will be characterized by membership functions. As the settlement area data have a bounding box for each section, therefore from that, a minimum and maximum limit of x and y coordinates have to be found. Assuming that Xmin, Xmax, Ymin and Ymax are lower-upper x limit and y limit respectively, the selection of the grid limit was: Xmin_selected ¼ 0.9 * Xmin Xmax_selected ¼ 1.1 * Xmax Ymin_selected ¼ 0.9 * Ymin Ymax_selected ¼ 1.1 * Ymax The mapping of the settlement area on the grid was performed as shown in Fig. 6. This step was repeated for all settlement areas as well as grid lines around the island. Mapping of the slope and wind speed was done by using an interpolation method, to find the parameter value on selected coordinates. It should be noted that this interpolation technique was used so as to avoid scattering of data (see Fig. 7). Each of the criteria under consideration (settlement areas, proximity to grid lines, slope and wind condition) was set up as fuzzy sets. The classification of the range of values corresponding to the different parameters of interest is summarized in Table 5. They are aggregated into single values based on the overall satisfaction degree using the AND operator. The impact index for each entity is computed and an overall index is assigned to the island of Mauritius (see Fig. 10 in results section). A triangular membership function was used for both solar and wind parameters as they are reported to achieve better performance accuracies as compared to other membership functions for variable parameters [51]. The trapezium membership function was used for settlement as a representative of the sharp drop-off at a

7

Fig. 7. Plot of sample points and interpolated values.

specific threshold value to reflect the inexistent value between 0 and 1. Finally, a Gaussian bell membership function was employed for slope constraint to highlight the smooth transition at the threshold limit value of 15
. The method implemented optimizes both accuracy and interpretability of the fuzzy logic network. An optimization algorithm has been integrated in the MATLAB™ programming environment to optimize the parameters of the membership functions belonging to the different fuzzy sets. Furthermore, the rule base is optimized by determining the optimum thresholds for interpretability betterment operation. Hence the method implemented optimizes the results. 3.4.3. Computational benefits of the method used Identification of optimum sites for installing hybrid wind-solar power plants is a costly procedure [52]. In addition to time and financial resources spent to acquire wind and solar insolation data on spatial scales, several other factors which include proximity to settlement areas and slope of the land need to be taken into account. Consequently, the study which permits identification and delineation of the optimum site boundary for dual wind and solar energy harnessing is both lengthy and costly. The main benefit of the method used in this work is that it offers a platform which enables the combination of multitude of parameters that are observed to influence the placement of the hybrid wind-solar farm. Another advantage of the method used is that even spatially distant data collected can be integrated in the model and processed since an interpolation technique is resorted to determine in-between missing values on spatial scales. An additional computational benefit is that the processing performed is very fast and accurate and saves the time for carrying individual regional combinational

Table 5 Classification of the range of values corresponding to different parameters of interest. Parameter

Fig. 6. Schematics for the AND operator.

Slope (o) Settlement area Wind (m/s) at 100 m Wind (m/s) at 60 m Solar(MJ/m2day)

Range of Values Reject

Average

Excellent

>15 1 <5 <5 <15

10e14 e 8e10 5.5e7.5 17e18

<10 0 >15 >7.5 22

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scenarios. The method employed does not have a lot of drawbacks apart from the fact that it requires good computational resources and relies on extensive computational memory to perform the GIS processing and amalgamation of the different influential factors.

 The map design adopted consisted of a map title situated at the topmost portion of each figure, accompanied by a legend describing the relevant details observed in the map. The energetic scale variations were also incorporated in the legend. Finally, all maps must have a scale bar and a north arrow regardless of the projection adopted [55].

3.5. Graphical representations 4. Results and discussions We employ in this study various graphical techniques in order to map the wind, solar and hybrid wind-solar energy resources of the country. The main graphical works studied are described as follows:  Digitization: It refers to the process of tracing the boundaries of geophysical bodies including rivers, reservoirs and core zone of world heritage site among others. Manual digitization is currently the most popular method of capturing coordinate data [53]. The manual digitization process was resorted to delineate the boundaries of geophysical bodies of interest on Google Earth software and was saved as a KML extension. The final stage involved converting the KML file into a vector layer in the ArcGIS environment.  Georeferencing: It is the process of aligning an image file with a spatially defined coordinate system [54]. This geographical processing technique came handy at a time when digitalized road and grid networks had to be rescaled and adjusted in the appropriate reference coordinate system. This method was performed in the ArcGIS platform and the digitalized and georeferenced files were overlain on the energy resource maps generated.  Geospatial analysis: One of the conditions imposed in the modelling stratagem being implemented is that the slope of the land need to be at an appropriate angle in order to facilitate the placement of solar photovoltaic panels and wind turbines. Slopes higher than 25
were derived from the digital elevation model and then overlain on the energy maps generated in order to reveal the unfeasible zones for development.

Influential factors dictating the location of solar farms within the island includes solar irradiation, slope factor, presence of settlement areas and proximity to grid lines. For the solar radiation parameter, insolation values of greater than 17 MJ/m2day were regarded as excellent criteria for solar farm construction. Consequently, as observed from Fig. 2(c), regions witnessing high solar irradiation includes the northern plains; part of the western to south-western flanks; and a spot region near the north-western region of the central plateau. The solar radiation parameter is regarded as highly influential in the fuzzy logic map for solar farming only. A slope factor of less than 15
was regarded as suitable for solar farm placement. Doorga et al. [33] rejected slopes of greater than 10
for solar farm optimization. However, the slightly greater angle of 15
would result in enhanced flexibility to the model performance. Additionally, the fuzzy model accounts for the presence of settlement zones which are regarded as unsuitable for solar farm location. The proximity to grid transmission lines is also included in the analysis to observe potential sites from an operational perspective. 4.1. Comparison and validation of results As illustrated from the fuzzy logic map generated (Fig. 8) for the case of wind farming at 60 m.a.g.l and 100 m.a.g.l, it is noted that the optimum sites for wind farming lie in the south-eastern region; south-western region; eastern part and north-western part of the central plateau. Those regions of high wind activity have been

Fig. 8. Fuzzy logic for wind farming at (a) 60 m.a.g.l. and (b) 100 m.a.g.l.

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Fig. 9. Wind rose for Mauritius [56].

confirmed by Dhunny et al. [32], which in perspective confirm the validity of the fuzzy logic analysis. A wind rose is displayed in Fig. 9 to show the wind direction. The region selected for the farm should have wind speeds between rated and cut-out speed of the wind turbines to be installed and should also be close to the grid transmission lines. It is interesting to note the intermediate to high potential of the regions of Bel Air in the eastern region, La LauraMalenga in the north-western plain of the central plateau and Le Morne in the South Western region. These regions show high suitability value, in addition to the appropriateness of land slope to accommodate construction. The validation of results with literature models are presented in Table 6. From the fuzzy logic map of Fig. 10 for solar farming only, it can be observed that the most suitable sites for solar farm placements lie in the northern; part of the western to south-western region; and north-western part of the central plateau. Consequently, it can be observed that the fuzzy logic map for solar farming only is highly responsive to the solar irradiation input values. In general, the northern and western halves of the island share the common feature of good solar resource potential for solar farm construction. The high suitability of the northern region is also reported by

Doorga et al. [33], which confirms the validity of the fuzzy logic system model implemented. It is also of interest to note that an intermediate solar regime is observed near the south-eastern region of Plaine Magnien. The southern and eastern regions of the island have inherently lower solar resource potential for construction of solar farms. The optimized solar map using fuzzy logic system is seen to generate a high degree of accuracy with solar maps generated by the Solargis (http://globalsolaratlas.info/). In another recent study undertaken by Doorga et al. [44] to map the solar photovoltaic potential of Mauritius, the high spatial correlation of the solar map produced by fuzzy logic system can be observed. In both maps, the northern and western regions of the island are observed to yield higher solar electricity output. The southern plains of the central plateau region is observed to record the lowest solar potential in all maps owing to cloud attenuation processes taking place as a result of forced advection of the South East Trade Wind upon encountering the rising slope of the central upland [44]. Consequently, the fuzzy model implemented is validated.

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Fig. 10. Fuzzy Logic showcasing site suitability for solar farming only.

wind solar farm. Both regions of interest are also near to grid transmission lines which increase the suitability of those sites for a hybrid wind solar farm. It is of interest to note the intermediate to high potential of the regions of Plaisance in the south-eastern region and Grand Sable in the far eastern region. Both regions have good solar and wind resource potentials in addition to the appropriateness of land slope to accommodate construction. Another observation is that at 60 m level (Fig. 11(a)), the suitability of sites for hybrid wind-solar farm construction increases on spatial extents as compared to the 100 m level (Fig. 11(b)). This is attributed to the higher (and therefore more suitable) wind conditions of the 60 m level over the spatial scale of the island as compared to the prevailing wind conditions at 100 m.a.g.l. Solar condition being practically a constant, implies that only wind factor that dictates the suitability of hybrid location for changes in height. The hybrid wind-solar maps are also validated since regions of high values are noted on spatial scales where the solar photovoltaic potential and the wind energy harnessing capacity are maximum. Also, low values are generated when both wind and solar potential are minimum. Intermediate values are computed whenever the combination of solar and wind gives rise to in-between values between the highest and lowest case scenarios observed. An appreciation of the sensitivity and robustness of the model can be observed from the selection preference plot of Fig. 12. The impact index was varied from 0.6 to 1.0 in order to observe the response of the fuzzy factors on the model performance. We have assumed the threshold value of 0.6 and above [45]. As can be inferred from Fig. 10, there are numerous regions which satisfy the 0.6 threshold. But we can only choose regions with proximity to grid lines. An impact index of 0.8 gives more limited regions for farming with focus on only the south-eastern region; southwestern region; eastern part and north-western part of the central plateau region of the island. Having tested the sensitivity of the fuzzy logic model, we further probe into the highly suitable sites identified by cross-referencing to aerial images of the island. Fig. 13 shows the best regions identified for the placement of a hybrid wind solar farm.

4.2. The hybrid wind-solar maps Fig. 11 presents the suitable regions for constructing hybrid wind-solar farms. The map was generated by combining wind speed, solar irradiation, slope factor, settlement areas and grid transmission lines via fuzzy logic system modelling. It can be observed that the northern and western regions on the country have higher potential for a hybrid wind-solar farm placement. This is due to the higher solar regime and intermediate to high wind regimes of the north-western region of Mauritius. The sites of highest suitability for hybrid wind solar farm placements are Le Morne located in the south western part and La Laura-Malenga situated in the north-western central plateau region. Both sites have inherently high solar and wind resource potential and as a consequence offer suitable climate for the placement of a hybrid

4.3. Energy analysis for the most appropriate identified site The best sites identified are Le Morne (Fig. 13 left) and La LauraMalenga (Fig. 13 right). The traced boundary for the selected suitable site of Le Morne was just outside the buffer zone of the World Heritage site. The boundaries of the core and buffer zones for the Le Morne World Heritage site were defined by the Ministry of Housing and Lands. The island of Mauritius has seen throughout the years, spells of colonial intervention, influencing cultural transformations in this region of the Indian Ocean. The history of the island is closely intertwined with slavery and indentured servitude who have contributed to its development and whose descendants form the majority of the present population. As a symbol of the resistance to slavery, Le Morne Cultural Landscape was officially declared World

Table 6 Validation of results with literature models. Parameter Validated literature model

Hybrid wind-solar model

Solar

Doorga et al. [44] generated a solar atlas using GIS multi- The hybrid wind-solar maps for both 60 m.a.g.l. and criteria modelling and noted the high solar potential of the 100 m.a.g.l. display very high potential on the northern plains of the country. northern plains of Mauritius.

Wind

Dhunny et al. [59] produced a wind map using CFD software and observed high wind potential in the southwestern, eastern and upper central plateau regions of the island.

The hybrid wind-solar maps for both 60 m.a.g.l. and 100 m.a.g.l. display notably high values in the southwestern, eastern and upper central plateau regions of Mauritius.

Validation Scale High validation scale due to similarity of peak values of hybrid wind-solar model with validated model in literature. High validation scale due to similarity of peak values of hybrid wind-solar model with validated model in literature.

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11

Fig. 11. Fuzzy logic for hybrid wind-solar farming at (a) 60 m.a.g.l. and (b) 100 m.a.g.l.

Fig. 12. Selection preference plot for different impact index for the hybrid wind solar farm (The impact index was varied from 0.6 to 1.0 in order to observe the response of the fuzzy factors on the model performance).

Heritage site by UNESCO. Strict laws protect this important site on the island. The core and buffer zones of the Le Morne Cultural Landscape are protected as a National Heritage site under the National Heritage Fund Act 2003 [57]. Another site of interest is La Laura-Malenga which is situated in the north-western plain of the central plateau. This site is

characterized as a region of high vegetation, with practically no settlement areas. The availability of land coupled with low settlement density added to the suitability of the site for a hybrid farm construction. It is of interest to note that both selected regions have been chosen based on their proximity to grid lines (as shown in Fig. 13) in addition to having an abundance of sunshine and wind.

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Fig. 13. The sites of interest for the construction of a hybrid wind solar farm: Le Morne (left) and La Laura-Malenga (right) (Illustration by Authors).

For both sites, the yearly solar electric power generation potential can be estimated [58] from equation (4) and tabulated in Table 7.

GP ¼ SR  CA  AF  h  CF  365

(4)

where GP : Yearly solar electric generation potential (GWh/year); SR : Yearly mean daily global solar irradiation (MJ/m2day); CA : Calculated total area of suitable land (m2), AF : Area factor which indicates the fraction (0.70) of calculated area that can be filled with solar panels; h : Efficiency of the PV solar panel (16%) and CF : Conversion factor (0.28) from MJ/m2year to kWh/m2year. For the wind farm, at Region A, a total of 70 wind turbines can be installed and for region B, 80 such turbines can be erected. These numbers were resulted from a previous article by the authors using Genetic algorithm for best wind turbine arrangements [59]. For this case we are using a Gamesa wind turbine at 60 m hub height with swept area 2642 m2. The annual power is calculated from equation (5) and summarized in Table 7.

1 P ¼ rAv3 Cp  8760; 2

(5)

where P is the yearly wind power generation (GWh/year); r is Air density; A is the swept area of wind turbine (m2); Cp is Power coefficient (0.1906 for this case of wind turbine) and 8760 is the number of hours in a year. The parameter description and solar electric generation potential of the two sites of interest in this study is summarized in Table 7.

4.4. Concept of solar tracking Solar tracking systems have been reported to improve the efficiency of photovoltaic modules, thereby increasing the electricity output of solar power plants. The performance of photovoltaic panels is largely influenced by the degree of overheating due to the excessive expose to solar irradiance in hot weather systems and countries situated near the tropical belt [60]. Eke et al. [61] reported that about 30% additional energy may be recovered after one year of continuous operation by a dual-axis solar tracking system as compared to a ground-mounted fixed system. A study undertaken to quantify the increase in efficiency from a single-axis solar tracker in the tropics showed that about 25% more power can be derived as compared to the fixed-axis configuration [62]. Consequently, the use of solar tracking systems will be beneficial to the overall energy harvested by the hybrid wind-solar farm to be potentially situated at the sites identified in this study. 5. Conclusions This paper explored the use of fuzzy-logic modeling to identify optimum locations for implementation of hybrid wind-solar farms on a complex topography terrain especially for Small Island Developing States (SIDS) which have limited land spaces. The decision model developed takes into account the local wind speed, solar radiation, slopes, settlement areas and proximity to grid lines. This enhanced mathematical model was successfully validated and applied to the island of Mauritius as a case study for which two regions: Le Morne and La Laura-Malenga, were identified as potential sites for the hybrid farming. The total observed generation

Table 7 Parameter description and solar electric generation potential of the two sites of interest. Site

A B

Region

Le Morne La Laura-Malenga

Area (m2)

310,829.4 370,199.9

Insolation (MJ/m2day)

17.07 16.73

Average Wind Speed (m/s)

9.2 7.2

Generation Potential (GWh/year) Solar

Wind

Total

60.73 70.89

100.85 210.39

161.58 281.28

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potential of energy per year for the hybrid farm is 161.58 GWh and 281.28 GWh respectively. The results conclude that fuzzy logic method yields better accuracy as compared with linear models. While this model was developed for SIDS, it can be used for other locations of varying scale with different terrain topography to achieve better return of investments through the combination of inshore renewable energy generation systems. The authors posit that this study can serve as a tool by Urban and Energy planners as an aid in choosing optimal renewable energy options based on site characteristics and constraints. Decision makers are thus equipped with a flexible framework for aggregating both qualitative and quantitative information.

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