Potential Map for the Installation of Concentrated Solar Power in Northeast of Brazil Using Analytic Hierarchy Process (AHP)

Brazil has a predominantly renewable energy matrix, with large participation of water resource in domestic supply of energy. Data from 2019 National Energy Balance show that renewable sources (water, biomass, wind and solar photovoltaic) together represented 83% of domestic electric supply in 2018, where the remaining percentage (16.7%) represented non-renewable sources. The generation of electricity through thermal solar technology was not rep-resentative. However, it is known that Brazil presents high potential for the installation of solar thermal plants, especially in the Northeastern Region, where direct normal solar irradiation values are high. It is observed that the (high) costs of the projects associated to the absence of a specific incentive program make Concentrating Solar Power (CSP) plants installation more and more time consuming. As a way to contribute to the insertion of solar thermal energy in Brazil, this article presents a methodology for the location of parabolic trough solar thermal plants of 80 MW for the State of Bahia, located in the Northeastern Region of Brazil. Such methodology was based on the application the Analytic Hierarchy Process (AHP) method and the Geoprocessing Technologies to define potentially available sites for the implementation of the projects. For the analysis, parameters related to energy production in the solar power plant, electric, roadways and water infrastructure of the plant were taken into account, as well as the occupation, slopes and land use. Considering the analyses performed, it was confirmed that Bahia disposes of many sites with great generation potential, especially in the western region of the State (at Barreiras), where favorable conditions were found for the development of the technology. Localities situated in other region of simplifications that were made.


Introduction
Currently, it is observed that solar thermal technology for the generation of electricity in Brazil is still incipient, without representation in the national energy

The AHP Method
The Analytic Hierarchy Process, or simply AHP Method, is one of the main methods of Multicriteria Decision Analysis (MDA). This method was developed by Thomas L. Saaty, in the mid-1980s, in order to obtain a general measurement theory to be used in the measurement of events in both physical and psychological domain.
The first step for the application of AHP method is to define the objective of the problem. According to [11], the objective of the method (or the problem to be solved) is a function to be developed and which structures the entire construction of the model. The objective can, in fact, define the decision rule to be used.
Once the objective is defined, the next step is the definition of the criteria and sub-criteria of the problem. The criteria allow the characterization of the main elements of a decision-making process and can be decomposed into sub-criteria.
The sub-criteria, in turn, can be determined by indicators that have the function of defining its magnitudes. The indicators are classified as positive when they do not restrict the potential of an alternative; and as negative (or restrictions) when they restrict the alternatives due to the activity to be developed [11].
After the objective definition and the construction of hierarchies, a paired comparison of the criteria is performed. To make this comparison [12] proposed the use of a measurement scale aiming for the standardization of judgments, which is presented in Table 1.
From the use of Saaty's Scale, the criteria are compared among themselves, originating a matrix of criteria comparison (Figure 1), that is, the elements a ij of this matrix represent the judgment given to each pair of evaluated criteria.
With the criteria comparison matrix defined, the standardization of its elements is made to estimate the weights of the criteria (w j ). One of the most used methods for this estimation is the Average of Normalized Columns, in which are performed the sum of the elements of each column of the Matrix (S 1 , S 2 , … S n ) to give rise to a new matrix, where each element is the result of the division of each element a ij of the matrix A by the sum of the corresponding column. As a last step of this procedure, the average of the normalized values of the rows is calculated, which corresponds to the values of the estimated weights.
After the definition of the criteria weights (global priority), the evaluation of the consistency of the model must be made in order to analyze the transitivity of the judged values. Such evaluation is made from the Consistency Ration (CR) which is calculated by Equations (1) and (2): where: CI = consistency index of judgments; RI = random consistency index; λ max = higher eigenvalue; and n = matrix order.
This random consistency index, parameter of Equation (1), was empirically determined considering a sample of 500 positive reciprocal matrices, randomly generated [11]. The values attributed to RI by [12], according to the matrix order (n), are shown in Table 2.
If the value found for the CR is greater or equal to 0.1, the judgment values in the criteria comparison matrix should be revised, as they are not sufficiently consistent to estimate the weights (w j ). In contrast, if such value is less than 0.1, the judged values are considered satisfactory [12].
Once the judged values are defined as consistent (global priority), the whole process of obtaining priorities should be repeated for the sub-criteria in order to establish its order of importance for the solution of the proposed problem. Also for these, the consistency analysis of the judged values should be carried out [11].

Geoprocessing Technologies Used in the Location Study in the State of Bahia
The term Geoprocessing emerged to group in a single name the several existing technologies that use geographic information. Among these technologies are included the GIS, Global Positioning Systems (GPS), Remote sensing, Geodesy, Journal of Geographic Information System

GIS
According to [14] GIS are computational systems developed for the purpose of digital processing of geographic information, considering its geometric, topologic and temporal aspects. They are composed by software resources developed to optimize the acquisition of geographic data, research and spatial analysis of geographic phenomena and facts, in addition to generating maps, letters, digital plants or various reports, achieving integration of geographic information at various thematic levels. In a social and technological perspective, the GIS is, in general, associated with institutional projects and requires qualified personnel for its operation, composing multidisciplinary work teams, with diverse and specific purposes.
In general, GIS may be represented as a network that links people to spatial data, through the use of hardware, software and procedure [15]. The software corresponds to computational programs used in GIS; The hardware corresponds to the computational platform used; The data comprise the geographic information that forms the Spatial Database (SD) of the system; The people represent the professionals responsible for the project, as well as system users. The procedures comprise the methodologies and the existent practical actions for the system to operate properly for the organization. For more details, see [15]. The operators of the Map Algebra treat the geographical fields as individual variables, layers, associating each geographic position of a determined study site to a qualitative or quantitative value, using expressions with well-defined syntax.

Fuzzy Logic
In location studies based on GIS and MDA, an important step is the normalization of spatial data. The normalization has the purpose of representing the spatial data values (originally not comparable to each other) in a continuous scale to allow the aggregation between them in the GIS environment. One of the most used techniques for normalization is fuzzy logic.
Fuzzy logic is based on the fuzzy sets theory, which represents classes of elements that do not have well defined frontiers [18]. The use of fuzzy sets is based on inference rules and is indicated for situations dealing with ambiguity, abstraction and ambivalence in mathematical or conceptual models of empirical phenomena [19]. Fuzzy membership functions represent the semantic properties of fuzzy sets and can present distinct formats (such as linear, triangular, trapezoidal, gaussian and sigmoidal functions). Greater details can be seen in [19] [20] [21].

Material Used
The materials used to carry out this research were: 1) Spring 5.2.6 (INPE) and

Methodology
The model used to approach the problem of solar thermal plants location in the State of Bahia was the AHP method. This method was chosen because, in addition to aggregating different criteria in a single function (which will be optimized), it has easy implementation and simple algorithm presentation. The stages of model elaboration are presented in Figure 3.    (Table 3) and restrictions (Table 4).

• Positive Indicators
According to Table 3, positive indicators refer to direct normal solar irradiation, slope, distance to power lines, distance to water resources, distance to main road, distance to urban areas and land use (except areas of high agricultural potential).

Slope Land Use
Decision Rule

Consistency Calculation
Objective  Direct normal solar irradiation is considered more important in the indication of potential sites for solar thermal plants installations, once it defines, quantitatively, the production of electricity of the solar power plant [22]. In fact, if we consider the flat-plate solar collector on the earth's surface tilted from a β angle in relation to the horizontal, the total solar irradiation (I h ) that reaches this plane at a given instant will be given by the sum of two components: direct and diffuse irradiation, such as shown in Equation (3) [5].

SPATIAL DATABASE
where: I c = solar irradiation on the surface of the collector; I bn = direct normal solar irradiation; θ = angle formed by the rays with the horizontal plane; I d = diffuse solar irradiation incident on the horizontal plane; β = edge angle; π = incidence angle; and C = geometric concentration.
Solar thermal power plants that present a geometric concentration ratio considered high, defined in the range of 50 < C < 100, for example, the diffuse contribution will reflect in a small fraction (negligible) of the solar irradiation incident on the surface of the collector, that is, the solar collector will see, practically, only the direct portion of solar irradiation incident on its surface ( cos c bn ). Therefore, the knowledge of direct normal solar irradiation in a given location is an essential factor for location studies.
The knowledge of land slope where the solar power plant will be installed is also an important factor for choosing the location, because it determines its impact on the costs for preparing and leveling the land. The ideal would be to have flat land, but with enough slope to allow the natural drainage of the land.
Regarding the distance to electric, water and road infrastructure elements, it is observed that the ideal is to have a proximity of the solar power plant with power lines, water resources and main roads in order to avoid increases to the total cost of the project in case of the necessity to build new pipelines or demand the expansion of power lines and existing road network to serve regions favorable to the implementation of the projects.
For urban and urban expansion areas, the issue of proximity is also a very important factor. For those, however, the ideal is that the solar power plant has a considerable distance from these regions, since both urban and urban expansion areas must be preserving in order to fulfill their social function (housing, work, recreation, circulation, among others).
Finally, with regard to land use, it is observed that the sites not used to productive purposes are more indicated for the installation of solar power plants. In this research, the sites considered as positive aspect in the model were those classified as: medium to high agricultural potential. On the other hand, the areas with high agricultural potential were considered as negative aspect in the model.        As can be seen in Figure 4, the direct normal solar irradiation indexes in Bahia range from 3.8 to 6.3 kWh/m 2 ·day (annual average According to the Map in Figure 5, it is observed that the highest slope percentages (higher than 4%) were mostly located in the Intermediate Geographic Regions of Feira de Santana, Salvador, Santo Antônio de Jesus, Vitória da Conquista and Ilhéus-Itabuna. Higher percentages can also be found in parts of In-termediate Geographic Regions of Guanambi, Irecê and Juazeiro. On the other hand, gentler slopes (0% -2%, 2% -4%) are located in the Intermediate Geographic Regions of Barreiras, Juazeiro, Irecê, Guanambi and Paulo Afonso. The land slope where Jaborandi Solar Power Plant is in the range of 0% -2%, which satisfies a great condition for project installation, once several authors [22] [23], indicate that maximum land slope for project installation should not be higher than 5%.
From the Map in Figure 6, it is verified that greater distances to power lines are located in the west of the State, especially in Intermediate Geographic Regions of Barreiras, Juazeiro and Irecê. In the neighboring area of Intermediate Geographic Regions of Juazeiro and Feira de Santana are also found large distances (above 60 km) between power lines. The region of Jaborandi Solar Power Plant is not contemplated by the Map, however, if an extension of the model is made for its region, it can be said that Jaborandi Solar Power Plant is located in a region of small distance to the power lines of 138 kV (0 -15 km), what also highlights a great criteria for the installation of CSP projects.
In the Map in Figure 7, it is observed that the greater distances to water resources in the State of Bahia are mainly located in the central areas of Intermediate Geographic Region of Paulo Afonso and at the border between Intermediate Geographic Regions of Salvador and Feira de Santana. Sill in this Map, it can be verified that Jaborandi Solar Power Plant is located in a region of small distance to permanent water resources (0 -15 km), which also shows a great criteria for the installation of CSP projects.
According to the Map shown in Figure 8, it is observed that greater distances to main roads are located in the Intermediate Geographic Region of Barreiras, in the extreme west of the State, and at the border between Intermediate Geographic Regions of Juazeiro and Irecê. In it, it is also observed that Jaborandi Solar Power Plant is located in a region of distances of 60 -75 km to the main roads (state and federal), which suggests that the access to the plant should be made by municipal roads or private roads in the region.
Regarding the Map in Figure 9, it is verified that the larger concentration of urban areas is located in the eastern portion of the State, mostly in the Intermediate Geographic Region of Salvador, and the greater distances to urban areas (above 60 km) are located in the extreme west of the State, in the Intermediate Geographic Region of Barreiras. In this respect, it is seen that Jaborandi Solar Power Plant is located in a region of great distances to the main urban centers of the State, which is also considered a great criteria for the installation of CSP projects.
Lastly, considering the Map in Figure 10, it is verified that the State has many sites with low or very low agricultural potential. On the other hand, high potential areas can be found in Intermediate Geographical Regions of Irecê, Guanambi, Paulo Afonso, Feira de Santana and Vitória da Conquista. In this regard, it is verified that Jaborandi Solar Power Plant is situated in a low agricultural potential area, which makes it propitious for the installation of CSP projects, once the Journal of Geographic Information System site is not used for productive purposes.

• Restrictions
The restrictions are related to those sites which activity or occupation must be preserved and controlled. In this study, the environments incorporated as restrictions are the following: Federal Conservation Units for Sustainable Use and Comprehensive Protection, Atlantic Forest Remnants; Indigenous Territories; Quilombola Territories; High Agricultural Potential Areas; Urban Areas; and Water Bodies, as illustrated in Figure 11.
From the Map presented in Figure 11, it is observed that there is a greater concentration of restriction areas in the southeastern and central portions of the State of Bahia.  Jaborandi Solar Power Plant is located in a region where no restrictions regarding land use are observed. This makes it suitable for the installation of CSP projects.

Decision Rule Definition
To evaluate the solar thermal power plant location problem in the State of Bahia, a Decision Rule was established for each one of the three scenarios developed for this study. In the first scenario, for example, the Climatic criteria was considered as most important for the decision rule. Following in order of importance, the Topographic, Environmental and Location criteria were defined, as shown in Figure 12.
A scenario without weights-Starting Point Scenario-was also generated to define the sites suitable for installation from the use of all indicators of the study (positive and restrictions), without considering the weights. It was also competed to this scenario to serve as reference to analyze the influence of weighting in the final result of each scenario created.

Weight Estimation and Model Consistency Calculation
After the establishment of the Decision Rule, the Weight Estimation for the problem criteria was carried out. Therefore, a paired comparison was performed between the pairs of criteria, using Saaty's Fundamental Scale, which gave rise to the Pairwise Comparison Matrix (Matrix A). This matrix was, then, normalized using the Average of Normalized Columns method to estimate the priority vectors (w j ). The step by step of this determination, for Scenario 1, is shown below: In Scenario 1, the Decision Rule adopted in order of importance was the sequence Climatic  Topographic  Environmental  Location, and then the pairwise comparison matrix had its format presented in Table 5. The normalization of this matrix is presented in Table 6.
Once obtained the priority vectors for the criteria, the Model Consistency Evaluation was carried out to verify transitivity of the judged values. The Consistency Ration calculation was made from the use of Equations (1) and (2) as well as the empirical value of Random Consistency Index equivalent to n = 4 (matrix order), shown in Table 2. The values found for the greater eigenvalue, the consistency index of judgments and consistency ration were, respectively, λ max = 4.045870784, CI = 0.015290261 and CR = 0.016989179. As the CR value was less than 0.10 (model request), the estimated values for the criteria were stated to be consistent.
With all the Scenario 1 criteria hierarchically organized, the entire process for obtaining the priorities vector and transitivity evaluation of the judged values was reproduced for the sub-criteria for the determination of final weights. Such final weights, as well as the λ max , CI and CR values calculated for the sub-criteria in Scenario 1, are presented in Table 7.   As the CR value was less than 0.10 (Table 7), the values judged for the sub-criteria were also stated as consistent.
In a similar way, the criteria and sub-criteria weights estimation were performed for Scenario 2 and 3, as well as the model consistency calculation. The Journal of Geographic Information System weights estimation and the values found of λ max , CI and CR for the sub-criteria of Scenarios 2 and 3 are presented, respectively, in Table 8 and Table 9.
As the CR value was less than 0.10 in Table 8 and Table 9, the estimated values for the sub-criteria were also stated as consistent.  To normalize the positive indicators, the sigmoidal fuzzy membership function was used, because, according to [21], the use of this function associated to a set of control points allows to properly represent the period in which the effect of the normalized value for the final result is more effective. The format of the sigmoidal fuzzy membership function is shown in Figure 13.

Presentation of the Scenarios
Contrary to the positive indicators that determine continuous surfaces for suitable sites, the restrictions (or negative indicators) present well defined limits, segmenting the classification of the sites as suitable and not suitable for a desired end. That way, the restrictions present a boolean format (binary nature) with suitability analysis given by: value one (1) when there is site suitability; and otherwise, the value zero (0).
The results found for the Starting Point Scenario is shown in Figure 14.
From the Map in Figure 14, it is seen that the greater availability of high sui- The results found for Scenario 1 are shown in Figure 15.
Looking at the Map in Figure 15 and comparing it to the Map in Figure 14    The results found for Scenario 2 are shown in Figure 16.
Looking at the Map in Figure 16 and comparing it to the Map in Figure 14, it can be seen that high suitability sites (class 7) were enlarged and now concen- The results found for Scenario 3 are shown in Figure 17.   In the last scenario of the study, Scenario 3, the Environmental criteria presented the higher weight against the other criteria in the study. In this configuration, the high suitability sites (classes 7 and 6) also concentrated in the IGR of Journal of Geographic Information System

Final Evaluation of the Scenarios
Barreiras, Juazeiro, Irecê and Guanambi, however they suffered a decrease in terms of number of locations. In this reality, these sites started to present an intermediate suitability (classes 4 and 5). This occurred because, in this configuration, the model "tended" to "pull" the sites classified as "low" and "very low" agricultural suitability to a high suitability group (classes 7 and 6), leaving the sites of "medium to high" agricultural suitability in the low suitability group (classes 1, 2 and 3).
The sites located in the south of the State did not present, in any of the scenarios of the study, much availability for the installation of projects since the site suitability found there was low in all scenarios (classes 1, 2 and 3). In addition, it is important to highlight that, regardless of the values associated to suitability classes, this region would be inadequate for the installation of projects because many of its sites are occupied by restriction areas.
In all the scenarios in this study it was also seen that the region of Jaborandi

Model Validation
The model validation process for this study was performed from the pix-

Conclusions
This article presented the results of the application of AHP methods for the location of parabolic trough solar thermal power plant of 80MW in the State of Bahia. Based on the performed analysis, it was verified that the location based on AHP method showed to be very adequate in providing subsidies aimed at the identification of potential sites. Also, it was confirmed that the State presents high potential for the development of solar thermal technology, especially in the Journal of Geographic Information System It is important to remember that the result of a GIS based analysis depends intrisically on the thematic layers used. If low quality spatial data are used, mistaken simplifications of reality may be generated, which will cause doubts and or uncertainties in the interpretation of the final results. Therefore, the use of high Journal of Geographic Information System quality spatial data will tend to provide more faithful and accurate representations of reality.
As a suggestion for future works, in order to improve the application of this methodology, it is proposed the conduction of new analyses with the incident direct normal solar irradiation, measured for at least five years; the evaluation of sites suitability without considering the water availability aspect for the plant, in the case of the possibility of using dry cooling systems in the solar power plants; and the on-site visit to ascertain the answers found by the GIS application.