1 Introduction

Renewable energy sources are the main composition of the Brazilian electricity matrix. According to Brazilian Electricity Regulatory Agency (ANEEL 2019), in the first quarter of 2019, it accounted for 87% of total production, while the remaining 13% were generated by fossil fuels. Despite the favorable rate, about 80% is concentrated in hydraulic sources. This dependency related to extreme climatic phenomena, such as drought, requires energy compensation by fossil fuels, pollutants and often more expensive (Souza & Cavalcante 2017).

An alternative is diversifying Brazil generation matrix with emerging technologies as concentrated solar power (CSP). Brazil registers normal direct solar irradiation (DNI) values above the minimum necessary for effective performance of CSP technologies (Souza & Cavalcante 2017). CSP by Cylinder-parabolic collectors (CCP) produces electrical energy by the concentration of solar energy in a thermodynamic cycle composed by three subsystems: solar field, thermal storage and power pack (Pereira et al. 2014).

The first steps of planning CSP plants is locating viable sites to construct and operate it, in which the viability can be determined by decision-making analysis of multiple criteria based on geographic attributes (Pereira et al. 2014). There are several methods of multi-criteria decision-analysis (MCDA), but not all of them integrate geospatial data and a large set of alternatives. TOPSIS and VIKOR are two well-know methods that use normalization and aggregation functions representing alternatives closeness to the ideal solution (Opricovic & Tzeng 2004). But, due to their aggregation function that treats each alternative at a time, it’s applied to a small set of alternatives compared to GIS based analysis. GIS based MCDA uses geographic information systems (GIS) to work with large areas represented by geospatial data (Greene et al. 2011; Malczewski 2006).

One of the first studies to locate sites to solar power plants using GIS based MCDA was to North Africa (Broesamle et al. 2001), in which regions were ranked by its estimation cost to construct the technology. Two criteria, DNI and slope, were selected with equal weights and classified with equal intervals by discretization. Fluri (2009) also analyzed the potential of solar power with 4 criteria, its geospatial data were classified in equal intervals with binarization and discretization, overlaying the maps with weighted linear combination - WLC. In these papers, discrete and continuous data were treated with discretization that breaks the transition zones between its distributions, which leads to misinterpretation of the data. A solution was applying normalization, in which transition zones were represented with normalized values (Clifton & Boruff 2010; Effat 2016). However, normalization creates an inconsistency due to the difference in the amplitude values of each criterion. Azevêdo, Candeias and Tiba (2017) and Mokarram et al. (2020) added an amplitude threshold to continuous data before normalizing it, controlling the intervals of the data and reducing inconsistencies. The threshold values were selected through literature and experts. Weights were obtained with AHP with processes in proprietary software. Table 1 brings characteristics of cited papers.

The mentioned studies used similar weighting, ranking and validating MCDA methodologies, although, to our knowledge, there isn’t a clear sequence of methods to apply GIS based MCDA with open source software. Because of this, the aim of this paper is to describe a detailed workflow with open source software of GIS based MCDA to locate viable sites to CSP plants in Brazil, validate and compare its results to another methodology and allow its replication to other technologies.

2 GIS Based AHP Methodology

2.1 Criteria Definition and Geospatial Data Acquisition

Firstly, the decision problem or main goal of the study must be set and the most important preconditions that lead to it, documented. For each precondition interpreted as a criterion, a geospatial data is obtained and standardized to the same geodetic reference system (GRS) and map projection.

2.2 AHP Weighting Method

GIS based AHP is a hybrid methodology of decision analysis. So, the five steps of classic AHP are applied to weight the criteria and the last two steps to rank the data are replaced by GIS approaches.

The classic AHP consists in a paired comparison of criteria applied with different levels of hierarchy to select the best alternatives (Saaty 2004). AHP can be applied through few steps: A. Define the decision problem or main goal of the study; B. Structure the decision-making hierarchy, starting from the top with the main goal, following with the most important criteria to reach the goal and subsequent lower level criteria, down to the last level where the alternatives are set; C. Construct pairwise matrices for each criteria level; D. Set the importance criteria values with experts opinion or indicators following the Fundamental Scale of Absolute Numbers; E. Calculate criteria weights and the matrix consistency; F. Compare alternatives according to each criterion; G. Rank the alternatives according to the objective.

The pairwise matrices can be structured on spreadsheets, in which each criterion is represented by a cell composed by a pair of line and column (Table 2). The expert’s opinion to fill the matrices usually are got with questionnaires to simplify the comparison between criteria, in which each comparison ‘line by column’ is one question. For example, to the cell (C₁, C₂) in Table 2, is applied a question: ‘How much (criterion 1) is more important than (criterion 2) to the objective?’ the answer value must be based on the fundamental scale of Saaty. The same is done to all cells on the top diagonal of each matrix. The bottoms of the diagonals were mirrored to the inverse of these values and the diagonals were composed by 1.

Weights to each criterion are defined by the eigenvector of the matrix (Equation 1). To ensure the consistency of the matrix values, the Consistency Ratio (CR) is calculated with Consistency Index (CI) and Randomness Index (RI) (Equation 2, 3 and 4). RI is obtained of an external table (Saaty 2004), according to the number of criteria of the respective matrix.

The CR should result within the interval suggested by Saaty (2004) of 0.1, which means that the process is consistent as it presents a maximum of 10% of inconsistency.

2.3 WLC Ranking Method

The GIS approach combines geospatial data with cartographic modeling and algebraic operators to rank the data. One of the most known models is WLC. It is applied to data structured in raster, in which each pixel had a location attribute with geographic coordinates and a numerical value that represents the feature. Then, the values of the pixels are normalized, and a weight is assigned to each image. The images are combined by map algebra resulting in a viability model (Malczewski 2000).

In WLC, the geospatial data must be in raster structure or transformed to it. The process called Rasterisation transform a vector feature into a raster with pixels values determined by a feature attribute value (Malczewski 2000). The feature attribute value can be set by many methods, three are described below:

A. Data attribute: Selecting single or multiples values from the data attribute table;

B. Binarization: Analyzing if the feature occurs in the cell, if it is true the pixel value is set to 1, otherwise, false, it is set to 0;

C. Proximity analysis: Binarization is applied as above, and after that, the distances from each pixel to pixels with value equal to 1 are calculated and a new value of the shortest distance is set to the pixel.

Interoperability between discrete and continuous data is ensured with normalization, which enables logical modeling from inaccurate data. However, it can mask discrepant amplitudes of data, as observed in previous studies. So, a threshold must be applied to the data amplitude, with fixed minimum and maximum values, reducing unwanted weights, and subsequently normalization is applied.

After that, the standardized data representing the criteria is combined by WLC (Equation 5).

2.4 Methods Validation

In addition to the AHP consistency, other validating methods based on comparative analysis can be proposed. Thematic accuracy is a validation method that compares same pixel in two different datasets, checking the percentage of similarity (IBGE 2017). Comparing the results obtained with the workflow to well-known methodologies based on different approaches, analyzing the trends and differences obtained. For both methods, points must be randomly sampled from the map as alternatives, and its criteria values are used to check the similarity and to calculate the ranking index with the methodologies.

2.4.1 VIKOR and TOPSIS, MCDA Ranking Methods

Two well-known not GIS based approaches are VIKOR and TOPSIS. VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) is a ranking method based on an aggregation of all criteria, the relative importance of the criteria, and a balance between total and individual satisfaction to determine the compromise solution. The aggregation function uses the proximity of the alternative to the ideal solution, in which the closer to the ideal solution, the better the alternative. The ranking index is a distance between two solutions distinguished by a weight applied to balance a majority decision by the decision makers or vetoes from a presence of conflicting criteria.

TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) is based on the distance from the ideal point and from the negative-ideal point. The method assumes that each criterion increases or decreases continuously until reaching its ideal and non-ideal value, maximum or minimum value of the criterion. Then, the Euclidean distance from the alternative criterion to both values are calculated. The best alternative must be next as possible of the ideal value and the worst alternative must be as far as possible. Finally, a similarity index between the best and the worst population distances are calculated, with values closest to 1 being ranked as the best alternatives (Opricovic & Tzeng 2004).

As it cannot be assumed that all criteria have the same importance, a weight can be applied to criteria in both methods. The main differences between them are the aggregation function as seen above and normalization function, where VIKOR uses linear normalization and TOPSIS uses vector normalization.

3 GIS Based MCDA Site Selection Framework: A case study of CSP in Brazil

In this work, GIS based AHP was applied to map Brazilian territory by its viability to the construction and operation of CSP by CCP technology. For that, preconditions were selected, classified as criteria (CR) and subcriteria (SC) and acquired as geospatial data. Then, criteria and subcriteria were weighted with AHP through parity matrices composed by online questionnaire created by the authors and applied to experts. Geospatial data treatment was done in open source software QGIS, in which the data was treated with diffuse logic and map algebra, resulting in a model of optimal site viability. Figure 1 describes the project workflow with stakeholders, MCDA, methods and tools applied.

3.1 Preconditions and Data Acquisition

In the definition of preconditions were analyzed 12 initial criteria, contemplating geographical, environmental and social attributes from a project of Brazilian Ministry of Science, Technology and Innovations (MCTI) with the German International Cooperation Agency (GIZ) (Pereira et al. 2014). From that, were chosen seven criteria composed by twenty three subcriteria based on characteristics of the Brazilian territory and the CSP technology, described on the first and second columns of Table 3. To each subcriteria were obtained a geospatial data and its metadata from reliable digital repositories and governmental data infrastructures, indicated in the third and fourth columns of Table 3.

3.2 Weighting Criteria with AHP

Parity matrices were made to subcriteria from criterion 3, 5 and 6 and between criteria. These were filled with experts opinions by questionnaires structured in a form template in free platform Jotform, available on https://www.jotform.com/form-templates/questionario-ahp. The form was organized in 5 pages: The first one contained an introduction to understand the methodology and instructions to fill the questions; the next four pages contained the four questionnaires with questions to the subcriteria and criteria. More than 34 forms were sent to experts, members of the project and externals. From these, 16 were selected based on its consistencies and according to the minimal forms suggested (Saaty 2004).

To fill the matrices were used the average of the answers of the 16 forms. To each parity matrix, the weights of the criteria or grouped subcriteria were calculated by the eigenvector of its corresponding line. The subcriteria global weight was obtained multiplying the grouped subcriteria weight by its respective criteria weight. The results are disposed on Table 4.

3.3 Ranking Alternatives with WLC and AHP

Firstly, geospatial data was projected to the geodetic reference system (GRS) SIRGAS 2000 and Polyconic map projection with central meridian at 54 degrees west. Data in vector structure was transformed to raster structure with rasterisation. The pixel size was set to 180 meters to satisfy a scale map of approximately 1:1.000.000.

The pixel value was obtained according to the precondition to be represented, with three methods: A. Data attribute: The data processed were Solar Irradiation, Slope, Land Use and Water Availability. For example, to solar irradiation the pixel value was collected from the annual average attribute on its attribute table. While, land use attributes were assigned to numeric values from 1 to 5; B. Binarization: The data processed was the restrictive criteria; C. Binarization + proximity analysis: In this process the pixel was set to 1 or 0, as above, and calculated the distance from each pixel set with 1, with Manhattan equation (which defines the distance between two points as the sum of the absolute differences between their coordinates). The data processed were the proximity of transmission lines, substations, urban areas, highways, railways, waterways and cargo airports.

The interoperability between the data was ensured setting the amplitude threshold and normalizing them. Firstly, the amplitude threshold values were applied to the rasterized data, with values from Table 3 specified with experts through the project guidelines (Küster et al. 2021). After that, discrete and continuous data were normalized by linear normalization. The standardized data for each subcriterion are presented in Figure 2.

The last step was combining the index from weight method with the ranking method (Equation 6). Each raster corresponding to a subcriterion (SC) was multiplied by its global weight (gw) and combined, then multiplied to the restrictions raster reduced from one, resulting in a new raster, the viability model.

Viability model = (DNI ^* 43.10 + Slope ^* 15.00 + Proximity to transmission lines ^* 8.49 + Proximity to substation ^* 11.96 + Proximity to urban areas ^* 1.93 + Water availability ^* 4.00 + Proximity to highways ^* 4.17 + Proximity to railways ^* 0.87 + Proximity to cargo airports ^* 0.43 + Proximity to waterways ^* 1.42 + Land use open areas / 1 ^* 4.02 + Land use pasture / 2 ^* 2.34 + Land use agricultural area / 3 ^* 1.04 + Land use sparse vegetation / 4 ^* 0.91 + Land use forest vegetation / 5 ^* 0.28) ^* (1 - Restrictions) (6)

3.4 Model Results and Validation

The result was a model with viability indices from 0 to 100%, restricted to ideal sites, to construct and operate CSP by CCP plants all over Brazil.

Figure 3 shows a large viability area to the technology mostly in Central-west, Southeast and Northeast of Brazil. Central-west and Southeast indices vary from 40% to 66%, while the Northeast brings the highest indices, reaching 70% in the state of Piauí (PI), and 80% in the state of Bahia (BA).

3.4.1 Model Consistency

The AHP consistency index was calculated from the average of each parity matrix, resulting in values of Table 5, in which the highest one is equal to 0.10 meaning a general consistency of 90%, in agreement with Saaty’s suggestion.

3.4.2 Thematic Accuracy of Standardized Data

Meanwhile, a validation of the data thematic accuracy was done pixel by pixel, comparing the standardized data index to another cartographic data external to the study (Table 6). Firstly, 80 areas with positive viability were randomly sampled and 20 manually in specific places. In each of the 100 areas, 5 items were sampled based on the 7 criteria (topography and water resources were not validated), resulting in 500 samples to compare with external data. Thereby, the validation obtained 96% of thematic accuracy.

3.4.3 Comparative Analysis of WLC, VIKOR and TOPSIS

In the comparative analysis were randomly sampled 10 points from the map as alternatives. Table 7 brings the alternatives indices and positions to the 3 methodologies.

For AHP+WLC and AHP+TOPSIS, the higher the index, the better, while for AHP+VIKOR, the lower the better. For ranking positions, all the methodologies follow the same tendency for first positions, with more similar results between AHP+CLP and AHP+VIKOR and some divergences compared to AHP+TOPSIS.

The results are directly related to the alternatives chosen due to the aggregation and normalization method, which are based on the amplitude of the values of the alternatives.

4 Conclusion

The methodology plays an important role as the first step in locating places to plants of CSP. The results showed that large regions in Brazil are viable to CSP plants. Still, more than 50% of the country's territories are not viable due to DNI indices below the experts suggested efficiency threshold of 1785 kWh/m²/year or because of environmental restrictions.

The workflow presented made clear how to apply the methodology. In AHP, the use of online questionnaires enabled the collaboration of experts from different regions of Brazil via internet. Yet, the high number of subcriteria in last questionnaire (seven) increased the accuracy needed in questionnaires consistency check, from 34 questionnaires applied, less than 20 accorded to the minimal consistency required. So, we advise sending questionnaires to twice as many as suggested by Saaty equation, or reducing the number of subcriteria in the same criteria hierarchy. Meanwhile, WLC method needs a well-defined workflow to standardize the data and reduce inconsistencies. Setting a threshold in amplitude of continuous data is necessary to avoid involuntary weights when normalizing multiple criteria. In addition, an expert opinion is crucial to set accurate threshold values.

The consistency of the final model was validated with AHP consistency accuracy of 90%. Besides that, the comparative analysis with 2 different MCDM not GIS based (TOPSIS and VIKOR) showed a good stability to the methodology with similar results and trend as the model values. AHP+TOPSIS got different values comparing to AHP+WLC and AHP+VIKOR, probably due to their normalize function differences, respectively vector and linear normalization.

Another important point was the application of the methodology with free and open source software QGIS, increasing accessibility and community discussion.

Therefore, as proposed, the methodology applied in free and open source software is an efficient method of decision-making to locate viable sites to construct and operate CSP plants and to help turning technologies from alternatives into plausible choices.

5 Acknowledgments

This research was supported by LACTEC - Instituto de tecnologia para o desenvolvimento, in collaboration with CESP - Companhia Energética de São Paulo, as a stage of the Strategic Research and Development project nº 019/2015 (PD-00061-0050/2016) of ANEEL - Agência Nacional de Energia Elétrica.

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Author notes

Corresponding author: Eduardo Chiarani; eduardo.chiarani@gmail.com